Skip to main content

2012 | OriginalPaper | Buchkapitel

5. Impulsive Partial Hyperbolic Functional Differential Equations

verfasst von : Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata

Erschienen in: Topics in Fractional Differential Equations

Verlag: Springer New York

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this chapter, we shall present existence results for some classes of initial value problems for fractional order partial hyperbolic differential equations with impulses at fixed or variable times impulses.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat M.I. Abbas, On the existence of locally attractive solutions of a nonlinear quadratic volterra integral equation of fractional order. Adv. Diff. Equ. 2010, 1–11 (2010)CrossRef M.I. Abbas, On the existence of locally attractive solutions of a nonlinear quadratic volterra integral equation of fractional order. Adv. Diff. Equ. 2010, 1–11 (2010)CrossRef
2.
Zurück zum Zitat S. Abbas, R.P. Agarwal, M. Benchohra, Darboux problem for impulsive partial hyperbolic differential equations of fractional order with variable times and infinite delay. Nonlinear Anal. Hybrid Syst. 4, 818–829 (2010)MathSciNetCrossRefMATH S. Abbas, R.P. Agarwal, M. Benchohra, Darboux problem for impulsive partial hyperbolic differential equations of fractional order with variable times and infinite delay. Nonlinear Anal. Hybrid Syst. 4, 818–829 (2010)MathSciNetCrossRefMATH
3.
Zurück zum Zitat S. Abbas, R.P. Agarwal, M. Benchohra, Impulsive discontinuous partial hyperbolic differential equations of fractional order on Banach Algebras. Electron. J. Differ. Equat. 2010(91), 1–17 (2010)MathSciNet S. Abbas, R.P. Agarwal, M. Benchohra, Impulsive discontinuous partial hyperbolic differential equations of fractional order on Banach Algebras. Electron. J. Differ. Equat. 2010(91), 1–17 (2010)MathSciNet
4.
Zurück zum Zitat S. Abbas, R.P. Agarwal, M. Benchohra, Existence theory for partial hyperbolic differential inclusions with finite delay involving the Caputo fractional derivative, (submitted) S. Abbas, R.P. Agarwal, M. Benchohra, Existence theory for partial hyperbolic differential inclusions with finite delay involving the Caputo fractional derivative, (submitted)
5.
Zurück zum Zitat S. Abbas, M. Benchohra, Partial hyperbolic differential equations with finite delay involving the Caputo fractional derivative. Commun. Math. Anal. 7, 62–72 (2009)MathSciNetMATH S. Abbas, M. Benchohra, Partial hyperbolic differential equations with finite delay involving the Caputo fractional derivative. Commun. Math. Anal. 7, 62–72 (2009)MathSciNetMATH
6.
Zurück zum Zitat S. Abbas, M. Benchohra, Darboux problem for perturbed partial differential equations of fractional order with finite delay. Nonlinear Anal. Hybrid Syst. 3, 597–604 (2009)MathSciNetCrossRefMATH S. Abbas, M. Benchohra, Darboux problem for perturbed partial differential equations of fractional order with finite delay. Nonlinear Anal. Hybrid Syst. 3, 597–604 (2009)MathSciNetCrossRefMATH
7.
Zurück zum Zitat S. Abbas, M. Benchohra, Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order. Nonlinear Anal. Hybrid Syst. 4, 406–413 (2010)MathSciNetCrossRefMATH S. Abbas, M. Benchohra, Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order. Nonlinear Anal. Hybrid Syst. 4, 406–413 (2010)MathSciNetCrossRefMATH
8.
Zurück zum Zitat S. Abbas, M. Benchohra, The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses. Discuss. Math. Differ. Incl. Control Optim. 30(1), 141–161 (2010)MathSciNetCrossRefMATH S. Abbas, M. Benchohra, The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses. Discuss. Math. Differ. Incl. Control Optim. 30(1), 141–161 (2010)MathSciNetCrossRefMATH
9.
Zurück zum Zitat S. Abbas, M. Benchohra, Impulsive partial hyperbolic differential inclusions of fractional order. Demonstratio Math. XLIII(4), 775–797 (2010) S. Abbas, M. Benchohra, Impulsive partial hyperbolic differential inclusions of fractional order. Demonstratio Math. XLIII(4), 775–797 (2010)
10.
Zurück zum Zitat S. Abbas, M. Benchohra, Darboux problem for partial functional differential equations with infinite delay and Caputo’s fractional derivative, Adv. Dynamical Syst. Appl. 5(1), 1–19 (2010)MathSciNet S. Abbas, M. Benchohra, Darboux problem for partial functional differential equations with infinite delay and Caputo’s fractional derivative, Adv. Dynamical Syst. Appl. 5(1), 1–19 (2010)MathSciNet
11.
Zurück zum Zitat S. Abbas, M. Benchohra, Impulsive partial hyperbolic functional differential equations of fractional order with state-dependent delay. Frac. Calc. Appl. Anal. 13(3), 225–244 (2010)MathSciNetMATH S. Abbas, M. Benchohra, Impulsive partial hyperbolic functional differential equations of fractional order with state-dependent delay. Frac. Calc. Appl. Anal. 13(3), 225–244 (2010)MathSciNetMATH
12.
Zurück zum Zitat S. Abbas, M. Benchohra, Upper and lower solutions method for the darboux problem for fractional order partial differential inclusions. Int. J. Modern Math. 5(3), 327–338 (2010)MathSciNetMATH S. Abbas, M. Benchohra, Upper and lower solutions method for the darboux problem for fractional order partial differential inclusions. Int. J. Modern Math. 5(3), 327–338 (2010)MathSciNetMATH
13.
Zurück zum Zitat S. Abbas, M. Benchohra, Existence theory for impulsive partial hyperbolic differential equations of fractional order at variable times. Fixed Point Theory. 12(1), 3–16 (2011)MathSciNetMATH S. Abbas, M. Benchohra, Existence theory for impulsive partial hyperbolic differential equations of fractional order at variable times. Fixed Point Theory. 12(1), 3–16 (2011)MathSciNetMATH
14.
Zurück zum Zitat S. Abbas, M. Benchohra, Upper and lower solutions method for partial hyperbolic functional differential equations with Caputo’s fractional derivative. Libertas Math. 31, 103–110 (2011)MathSciNetMATH S. Abbas, M. Benchohra, Upper and lower solutions method for partial hyperbolic functional differential equations with Caputo’s fractional derivative. Libertas Math. 31, 103–110 (2011)MathSciNetMATH
15.
Zurück zum Zitat S. Abbas, M. Benchohra, Existence results for fractional order partial hyperbolic functional differential inclusions, (submitted) S. Abbas, M. Benchohra, Existence results for fractional order partial hyperbolic functional differential inclusions, (submitted)
16.
Zurück zum Zitat S. Abbas, M. Benchohra, A global uniqueness result for fractional order implicit differential equations. Math. Univ. Comen (submitted) S. Abbas, M. Benchohra, A global uniqueness result for fractional order implicit differential equations. Math. Univ. Comen (submitted)
17.
Zurück zum Zitat S. Abbas, M. Benchohra, Darboux problem for implicit impulsive partial hyperbolic differential equations. Electron. J. Differ. Equat. 2011, 15 (2011)MathSciNet S. Abbas, M. Benchohra, Darboux problem for implicit impulsive partial hyperbolic differential equations. Electron. J. Differ. Equat. 2011, 15 (2011)MathSciNet
18.
Zurück zum Zitat S. Abbas, M. Benchohra, On the set of solutions of fractional order Riemann-Liouville integral inclusions. Demonstratio Math. (to appear) S. Abbas, M. Benchohra, On the set of solutions of fractional order Riemann-Liouville integral inclusions. Demonstratio Math. (to appear)
19.
Zurück zum Zitat S. Abbas, M. Benchohra, On the set of solutions for the Darboux problem for fractional order partial hyperbolic functional differential inclusions. Fixed Point Theory (to appear) S. Abbas, M. Benchohra, On the set of solutions for the Darboux problem for fractional order partial hyperbolic functional differential inclusions. Fixed Point Theory (to appear)
20.
Zurück zum Zitat S. Abbas, M. Benchohra, Uniqueness results for Fredholm type fractional order Riemann-Liouville integral equations (submitted) S. Abbas, M. Benchohra, Uniqueness results for Fredholm type fractional order Riemann-Liouville integral equations (submitted)
21.
Zurück zum Zitat S. Abbas, M. Benchohra, Fractional order Riemann-Liouville integral equations with multiple time delay. Appl. Math. E-Notes (to appear) S. Abbas, M. Benchohra, Fractional order Riemann-Liouville integral equations with multiple time delay. Appl. Math. E-Notes (to appear)
22.
Zurück zum Zitat S. Abbas, M. Benchohra, Nonlinear quadratic Volterra Riemann-Liouville integral equations of fractional order. Nonlinear Anal. Forum 17, 1–9 (2012) S. Abbas, M. Benchohra, Nonlinear quadratic Volterra Riemann-Liouville integral equations of fractional order. Nonlinear Anal. Forum 17, 1–9 (2012)
23.
Zurück zum Zitat S. Abbas, M. Benchohra, On the set of solutions of nonlinear fractional order Riemann-Liouville functional integral equations in Banach algebras (submitted) S. Abbas, M. Benchohra, On the set of solutions of nonlinear fractional order Riemann-Liouville functional integral equations in Banach algebras (submitted)
24.
Zurück zum Zitat S. Abbas, M. Benchohra, Fractional order Riemann-Liouville integral inclusions with two independent variables and multiple time delay. Opuscula Math. (to appear) S. Abbas, M. Benchohra, Fractional order Riemann-Liouville integral inclusions with two independent variables and multiple time delay. Opuscula Math. (to appear)
25.
Zurück zum Zitat S. Abbas, M. Benchohra, L. Gorniewicz, Existence theory for impulsive partial hyperbolic functional differential equations involving the Caputo fractional derivative. Sci. Math. Jpn.. online e- 2010, 271–282 S. Abbas, M. Benchohra, L. Gorniewicz, Existence theory for impulsive partial hyperbolic functional differential equations involving the Caputo fractional derivative. Sci. Math. Jpn.. online e- 2010, 271–282
26.
Zurück zum Zitat S. Abbas, M. Benchohra, L. Gorniewicz, Fractional order impulsive partial hyperbolic differential inclusions with variable times. Discussions Mathe. Differ. Inclu. Contr. Optimiz. 31(1), 91–114 (2011)MathSciNetCrossRefMATH S. Abbas, M. Benchohra, L. Gorniewicz, Fractional order impulsive partial hyperbolic differential inclusions with variable times. Discussions Mathe. Differ. Inclu. Contr. Optimiz. 31(1), 91–114 (2011)MathSciNetCrossRefMATH
27.
Zurück zum Zitat S. Abbas, M. Benchohra, L. Gorniewicz, Fractional order impulsive partial hyperbolic functional differential equations with variable times and state-dependent delay. Math. Bulletin 7, 317–350 (2010) S. Abbas, M. Benchohra, L. Gorniewicz, Fractional order impulsive partial hyperbolic functional differential equations with variable times and state-dependent delay. Math. Bulletin 7, 317–350 (2010)
28.
Zurück zum Zitat S. Abbas, M. Benchohra, J. Henderson, Global asymptotic stability of solutions of nonlinear quadratic Volterra integral equations of fractional order. Comm. Appl. Nonlinear Anal. 19, 79–89 (2012)MathSciNetMATH S. Abbas, M. Benchohra, J. Henderson, Global asymptotic stability of solutions of nonlinear quadratic Volterra integral equations of fractional order. Comm. Appl. Nonlinear Anal. 19, 79–89 (2012)MathSciNetMATH
29.
Zurück zum Zitat S. Abbas, M. Benchohra, J. Henderson, Attractivity results for nonlinear fractional order Riemann-Liouville integral equations in Banach algebras, (submitted) S. Abbas, M. Benchohra, J. Henderson, Attractivity results for nonlinear fractional order Riemann-Liouville integral equations in Banach algebras, (submitted)
30.
Zurück zum Zitat S. Abbas, M. Benchohra, J.J. Nieto, Global uniqueness results for fractional order partial hyperbolic functional differential equations. Adv. in Difference Equ. 2011, Art. ID 379876, 25 pp S. Abbas, M. Benchohra, J.J. Nieto, Global uniqueness results for fractional order partial hyperbolic functional differential equations. Adv. in Difference Equ. 2011, Art. ID 379876, 25 pp
31.
Zurück zum Zitat S. Abbas, M. Benchohra, J.J. Nieto, Functional implicit hyperbolic fractional order differential equations with delay, (submitted) S. Abbas, M. Benchohra, J.J. Nieto, Functional implicit hyperbolic fractional order differential equations with delay, (submitted)
32.
Zurück zum Zitat S. Abbas, M. Benchohra, G.M. N’Guérékata, B.A. Slimani, Darboux problem for fractional order discontinuous hyperbolic partial differential equations in Banach algebras. Complex Variables and Elliptic Equations 57(2–4), 337–350 (2012)MathSciNetCrossRefMATH S. Abbas, M. Benchohra, G.M. N’Guérékata, B.A. Slimani, Darboux problem for fractional order discontinuous hyperbolic partial differential equations in Banach algebras. Complex Variables and Elliptic Equations 57(2–4), 337–350 (2012)MathSciNetCrossRefMATH
33.
Zurück zum Zitat S. Abbas, M. Benchohra, J.J. Trujillo, Fractional order impulsive hyperbolic implicit differential equations with state-dependent delay (submitted) S. Abbas, M. Benchohra, J.J. Trujillo, Fractional order impulsive hyperbolic implicit differential equations with state-dependent delay (submitted)
34.
Zurück zum Zitat S. Abbas, M. Benchohra, A.N. Vityuk, On fractional order derivatives and Darboux problem for implicit differential equations. Frac. Calc. Appl. Anal. 15(2), 168–182 (2012)MathSciNet S. Abbas, M. Benchohra, A.N. Vityuk, On fractional order derivatives and Darboux problem for implicit differential equations. Frac. Calc. Appl. Anal. 15(2), 168–182 (2012)MathSciNet
35.
Zurück zum Zitat S. Abbas, M. Benchohra, Y. Zhou, Darboux problem for fractional order neutral functional partial hyperbolic differential equations, Int. J. Dynamical Systems Differential Equations. 2(3&4), 301–312 (2009)MathSciNetCrossRefMATH S. Abbas, M. Benchohra, Y. Zhou, Darboux problem for fractional order neutral functional partial hyperbolic differential equations, Int. J. Dynamical Systems Differential Equations. 2(3&4), 301–312 (2009)MathSciNetCrossRefMATH
36.
Zurück zum Zitat S. Abbas, M. Benchohra, Y. Zhou, Fractional order partial functional differential inclusions with infinite delay. Proc. A. Razmadze Math. Inst. 154, 1–19 (2010)MathSciNetMATH S. Abbas, M. Benchohra, Y. Zhou, Fractional order partial functional differential inclusions with infinite delay. Proc. A. Razmadze Math. Inst. 154, 1–19 (2010)MathSciNetMATH
37.
Zurück zum Zitat S. Abbas, M. Benchohra, Y. Zhou, Fractional order partial hyperbolic functional differential equations with state-dependent delay. Int. J. Dyn. Syst. Differ. Equat. 3(4), 459–490 (2011)MathSciNetMATH S. Abbas, M. Benchohra, Y. Zhou, Fractional order partial hyperbolic functional differential equations with state-dependent delay. Int. J. Dyn. Syst. Differ. Equat. 3(4), 459–490 (2011)MathSciNetMATH
38.
Zurück zum Zitat N.H. Abel, Solutions de quelques problèmes à l’aide d’intégrales définies (1823). Œuvres complètes de Niels Henrik Abel, 1, Grondahl, Christiania, 1881, 11–18 N.H. Abel, Solutions de quelques problèmes à l’aide d’intégrales définies (1823). Œuvres complètes de Niels Henrik Abel, 1, Grondahl, Christiania, 1881, 11–18
39.
Zurück zum Zitat R.P Agarwal, M. Benchohra, S. Hamani, Boundary value problems for fractional differential equations. Georgian. Math. J. 16, 401–411 (2009) R.P Agarwal, M. Benchohra, S. Hamani, Boundary value problems for fractional differential equations. Georgian. Math. J. 16, 401–411 (2009)
40.
Zurück zum Zitat R.P Agarwal, M. Benchohra, S. Hamani, A survey on existence result for boundary value problems of nonlinear fractional differential equations and inclusions. Acta. Appl. Math. 109, 973–1033 (2010) R.P Agarwal, M. Benchohra, S. Hamani, A survey on existence result for boundary value problems of nonlinear fractional differential equations and inclusions. Acta. Appl. Math. 109, 973–1033 (2010)
41.
Zurück zum Zitat R.P. Agarwal, M. Benchohra, B.A. Slimani, Existence results for differential equations with fractional order and impulses. Mem. Differ. Equat. Math. Phys. 44, 1–21 (2008)MathSciNetMATH R.P. Agarwal, M. Benchohra, B.A. Slimani, Existence results for differential equations with fractional order and impulses. Mem. Differ. Equat. Math. Phys. 44, 1–21 (2008)MathSciNetMATH
42.
Zurück zum Zitat R.P. Agarwal, M. Meehan, D. O’Regan, Fixed Point Theory and Applications, in Cambridge Tracts in Mathematics, vol. 141 (Cambridge University Press, Cambridge, 2001)CrossRef R.P. Agarwal, M. Meehan, D. O’Regan, Fixed Point Theory and Applications, in Cambridge Tracts in Mathematics, vol. 141 (Cambridge University Press, Cambridge, 2001)CrossRef
43.
Zurück zum Zitat R.P. Agarwal, D. ORegan, S. Stanek, Positive solutions for Dirichlet problem of singular nonlinear fractional differential equations. J. Math. Anal. Appl. 371, 57–68 (2010) R.P. Agarwal, D. ORegan, S. Stanek, Positive solutions for Dirichlet problem of singular nonlinear fractional differential equations. J. Math. Anal. Appl. 371, 57–68 (2010)
44.
Zurück zum Zitat R.P Agarwal, Y. Zhou, Y. He, Existence of fractional neutral functional differential equations. Comput. Math. Appl. 59(3), 1095–1100 (2010) R.P Agarwal, Y. Zhou, Y. He, Existence of fractional neutral functional differential equations. Comput. Math. Appl. 59(3), 1095–1100 (2010)
45.
Zurück zum Zitat R.P. Agarwal, Y. Zhou, J. Wang, X. Luo, Fractional functional differential equations with causal operators in Banach spaces. Math. Comput. Model. 54(5–6), 1440–1452 (2011)MathSciNetCrossRefMATH R.P. Agarwal, Y. Zhou, J. Wang, X. Luo, Fractional functional differential equations with causal operators in Banach spaces. Math. Comput. Model. 54(5–6), 1440–1452 (2011)MathSciNetCrossRefMATH
46.
Zurück zum Zitat O.P. Agrawal, O. Defterli, D. Baleanu, Fractional optimal control problems with several state and control variables. J. Vib. Contr. 16(13), 1967–1976 (2010)MathSciNetCrossRef O.P. Agrawal, O. Defterli, D. Baleanu, Fractional optimal control problems with several state and control variables. J. Vib. Contr. 16(13), 1967–1976 (2010)MathSciNetCrossRef
47.
Zurück zum Zitat B. Ahmad, J.J. Nieto, Existence of solutions for impulsive anti-periodic boundary value problems of fractional order. Taiwanese J. Math. 15(3), 981–993 (2011)MathSciNetMATH B. Ahmad, J.J. Nieto, Existence of solutions for impulsive anti-periodic boundary value problems of fractional order. Taiwanese J. Math. 15(3), 981–993 (2011)MathSciNetMATH
48.
Zurück zum Zitat B. Ahmad, S. Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations. Nonlinear Anal. Hybrid Syst. 3, 251–258 (2009)MathSciNetCrossRefMATH B. Ahmad, S. Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations. Nonlinear Anal. Hybrid Syst. 3, 251–258 (2009)MathSciNetCrossRefMATH
49.
Zurück zum Zitat E. Ait Dads, M. Benchohra, S. Hamani, Impulsive fractional differential inclusions involving the Caputo fractional derivative. Fract. Calc. Appl. Anal. 12(1), 15–38 (2009)MathSciNetMATH E. Ait Dads, M. Benchohra, S. Hamani, Impulsive fractional differential inclusions involving the Caputo fractional derivative. Fract. Calc. Appl. Anal. 12(1), 15–38 (2009)MathSciNetMATH
50.
Zurück zum Zitat R. Almeida, D.F.M. Torres, Fractional variational calculus for nondifferentiable functions. Comput. Math. Appl. 61, 3097–3104 (2011)MathSciNetCrossRefMATH R. Almeida, D.F.M. Torres, Fractional variational calculus for nondifferentiable functions. Comput. Math. Appl. 61, 3097–3104 (2011)MathSciNetCrossRefMATH
51.
Zurück zum Zitat R. Almeida, D.F.M. Torres, Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives. Commun. Nonlinear Sci. Numer. Simul. 16, 1490–1500 (2011)MathSciNetCrossRefMATH R. Almeida, D.F.M. Torres, Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives. Commun. Nonlinear Sci. Numer. Simul. 16, 1490–1500 (2011)MathSciNetCrossRefMATH
52.
Zurück zum Zitat G.A. Anastassiou, in Advances on Fractional Inequalities (Springer, New York, 2011) G.A. Anastassiou, in Advances on Fractional Inequalities (Springer, New York, 2011)
53.
Zurück zum Zitat D. Araya, C. Lizama, Almost automorphic mild solutions to fractional differential equations. Nonlinear Anal. 69, 3692–3705 (2008)MathSciNetCrossRefMATH D. Araya, C. Lizama, Almost automorphic mild solutions to fractional differential equations. Nonlinear Anal. 69, 3692–3705 (2008)MathSciNetCrossRefMATH
54.
55.
Zurück zum Zitat J.P. Aubin, Impulse differential inclusions and hybrid systems: a viability ap- proach, Lecture Notes, Universit Paris-Dauphine (2002) J.P. Aubin, Impulse differential inclusions and hybrid systems: a viability ap- proach, Lecture Notes, Universit Paris-Dauphine (2002)
56.
Zurück zum Zitat J.P. Aubin, A. Cellina, in Differential Inclusions (Springer, Berlin, 1984) J.P. Aubin, A. Cellina, in Differential Inclusions (Springer, Berlin, 1984)
57.
Zurück zum Zitat J.P. Aubin, H. Frankowska, in Set-Valued Analysis (Birkhauser, Boston, 1990) J.P. Aubin, H. Frankowska, in Set-Valued Analysis (Birkhauser, Boston, 1990)
58.
Zurück zum Zitat I. Bajo, E. Liz, Periodic boundary value problem for first order differential equations with impulses at variable times. J. Math. Anal. Appl. 204, 65–73 (1996)MathSciNetCrossRefMATH I. Bajo, E. Liz, Periodic boundary value problem for first order differential equations with impulses at variable times. J. Math. Anal. Appl. 204, 65–73 (1996)MathSciNetCrossRefMATH
59.
Zurück zum Zitat K. Balachandran, S. Kiruthika, J.J. Trujillo, Existence results for fractional impulsive integrodifferetial equations in Banach spaces. Comm. Nonlinear Sci. Numer. Simul. 16, 1970–1977 (2011)MathSciNetCrossRefMATH K. Balachandran, S. Kiruthika, J.J. Trujillo, Existence results for fractional impulsive integrodifferetial equations in Banach spaces. Comm. Nonlinear Sci. Numer. Simul. 16, 1970–1977 (2011)MathSciNetCrossRefMATH
60.
Zurück zum Zitat K. Balachandran, J.J. Trujillo, The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces. Nonlinear Anal. 72, 4587-4593 (2010)MathSciNetCrossRefMATH K. Balachandran, J.J. Trujillo, The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces. Nonlinear Anal. 72, 4587-4593 (2010)MathSciNetCrossRefMATH
61.
Zurück zum Zitat D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, in Fractional Calculus Models and Numerical Methods (World Scientific Publishing, New York, 2012) D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, in Fractional Calculus Models and Numerical Methods (World Scientific Publishing, New York, 2012)
62.
Zurück zum Zitat D. Baleanu, S.I. Vacaru, Fractional curve flows and solitonic hierarchies in gravity and geometric mechanics. J. Math. Phys. 52(5), 053514, 15 (2011) D. Baleanu, S.I. Vacaru, Fractional curve flows and solitonic hierarchies in gravity and geometric mechanics. J. Math. Phys. 52(5), 053514, 15 (2011)
63.
Zurück zum Zitat J. Banaś, B.C. Dhage, Global asymptotic stability of solutions of a functional integral equation. Nonlinear Anal. 69(7), 1945–1952 (2008)MathSciNetCrossRefMATH J. Banaś, B.C. Dhage, Global asymptotic stability of solutions of a functional integral equation. Nonlinear Anal. 69(7), 1945–1952 (2008)MathSciNetCrossRefMATH
64.
Zurück zum Zitat E. Bazhlekova, in Fractional Evolution Equations in Banach Spaces (University Press Facilities, Eindhoven University of Technology, 2001) E. Bazhlekova, in Fractional Evolution Equations in Banach Spaces (University Press Facilities, Eindhoven University of Technology, 2001)
65.
Zurück zum Zitat A. Belarbi, M. Benchohra, Existence theory for perturbed impulsive hyperbolic differential inclusions with variable times. J. Math. Anal. Appl. 327, 1116–1129 (2007)MathSciNetCrossRefMATH A. Belarbi, M. Benchohra, Existence theory for perturbed impulsive hyperbolic differential inclusions with variable times. J. Math. Anal. Appl. 327, 1116–1129 (2007)MathSciNetCrossRefMATH
66.
Zurück zum Zitat A. Belarbi, M. Benchohra, A. Ouahab, Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces. Appl. Anal. 85, 1459–1470 (2006)MathSciNetCrossRefMATH A. Belarbi, M. Benchohra, A. Ouahab, Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces. Appl. Anal. 85, 1459–1470 (2006)MathSciNetCrossRefMATH
67.
Zurück zum Zitat M. Benchohra, J.R. Graef, S. Hamani, Existence results for boundary value problems of nonlinear fractional differential equations with integral conditions. Appl. Anal. 87(7), 851–863 (2008)MathSciNetCrossRefMATH M. Benchohra, J.R. Graef, S. Hamani, Existence results for boundary value problems of nonlinear fractional differential equations with integral conditions. Appl. Anal. 87(7), 851–863 (2008)MathSciNetCrossRefMATH
68.
Zurück zum Zitat M. Benchohra, J.R. Graef, F-Z. Mostefai, Weak solutions for nonlinear fractional differential equations on reflexive Banach spaces. Electron. J. Qual. Theory Differ. Equat. 2010(54), 10 pp M. Benchohra, J.R. Graef, F-Z. Mostefai, Weak solutions for nonlinear fractional differential equations on reflexive Banach spaces. Electron. J. Qual. Theory Differ. Equat. 2010(54), 10 pp
69.
Zurück zum Zitat M. Benchohra, S. Hamani, S.K. Ntouyas, boundary value problems for differential equations with fractional order. Surv. Math. Appl. 3, 1–12 (2008)MathSciNetMATH M. Benchohra, S. Hamani, S.K. Ntouyas, boundary value problems for differential equations with fractional order. Surv. Math. Appl. 3, 1–12 (2008)MathSciNetMATH
70.
Zurück zum Zitat M. Benchohra, J. Henderson, S.K. Ntouyas, in Impulsive Differential Equations and Inclusions, vol. 2 (Hindawi Publishing Corporation, New York, 2006) M. Benchohra, J. Henderson, S.K. Ntouyas, in Impulsive Differential Equations and Inclusions, vol. 2 (Hindawi Publishing Corporation, New York, 2006)
71.
Zurück zum Zitat M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, Existence results for functional differential equations of fractional order. J. Math. Anal. Appl. 338, 1340–1350 (2008)MathSciNetCrossRefMATH M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, Existence results for functional differential equations of fractional order. J. Math. Anal. Appl. 338, 1340–1350 (2008)MathSciNetCrossRefMATH
72.
Zurück zum Zitat M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, On first order impulsive dynamic equations on time scales. J. Difference Equ. Appl. 10, 541–548 (2004)MathSciNetCrossRefMATH M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, On first order impulsive dynamic equations on time scales. J. Difference Equ. Appl. 10, 541–548 (2004)MathSciNetCrossRefMATH
73.
Zurück zum Zitat M. Benchohra, J.J. Nieto, D. Seba, Measure of noncompactness and hyperbolic partial fractional differential equations in Banach spaces. Panamer. Math. J. 20(3), 27–37 (2010)MathSciNetMATH M. Benchohra, J.J. Nieto, D. Seba, Measure of noncompactness and hyperbolic partial fractional differential equations in Banach spaces. Panamer. Math. J. 20(3), 27–37 (2010)MathSciNetMATH
74.
Zurück zum Zitat M. Benchohra, S.K. Ntouyas, An existence theorem for an hyperbolic differential inclusion in Banach spaces. Discuss. Math. Differ. Incl. Contr. Optim. 22, 5–16 (2002)MathSciNetCrossRefMATH M. Benchohra, S.K. Ntouyas, An existence theorem for an hyperbolic differential inclusion in Banach spaces. Discuss. Math. Differ. Incl. Contr. Optim. 22, 5–16 (2002)MathSciNetCrossRefMATH
75.
Zurück zum Zitat M. Benchohra, S.K. Ntouyas, On an hyperbolic functional differential inclusion in Banach spaces. Fasc. Math. 33, 27–35 (2002)MathSciNetMATH M. Benchohra, S.K. Ntouyas, On an hyperbolic functional differential inclusion in Banach spaces. Fasc. Math. 33, 27–35 (2002)MathSciNetMATH
76.
Zurück zum Zitat M. Benchohra, S.K. Ntouyas, An existence result for hyperbolic functional differential inclusions. Comment. Math. Prace Mat. 42, 1–16 (2002)MathSciNetMATH M. Benchohra, S.K. Ntouyas, An existence result for hyperbolic functional differential inclusions. Comment. Math. Prace Mat. 42, 1–16 (2002)MathSciNetMATH
77.
Zurück zum Zitat M. Benchohra, B.A. Slimani, Existence and uniqueness of solutions to impulsive fractional differential equations. Electron. J. Differ. Equat. 2009(10), 11 (2009) M. Benchohra, B.A. Slimani, Existence and uniqueness of solutions to impulsive fractional differential equations. Electron. J. Differ. Equat. 2009(10), 11 (2009)
78.
Zurück zum Zitat F. Berhoun, A contribution of some classes of impulsive differential equations with integer and non integer order, Doctorate thesis, University of Sidi Bel Abbes, 2010 F. Berhoun, A contribution of some classes of impulsive differential equations with integer and non integer order, Doctorate thesis, University of Sidi Bel Abbes, 2010
79.
Zurück zum Zitat A. Bica, V.A. Caus, S. Muresan, Application of a trapezoid inequality to neutral Fredholm integro-differential equations in Banach spaces. J. Inequal. Pure Appl. Math. 7, 5 (2006), Art. 173 A. Bica, V.A. Caus, S. Muresan, Application of a trapezoid inequality to neutral Fredholm integro-differential equations in Banach spaces. J. Inequal. Pure Appl. Math. 7, 5 (2006), Art. 173
80.
Zurück zum Zitat F.S. De Blasi, G. Pianigiani, V. Staicu: On the solution sets of some nonconvex hyperbolic differential inclusions. Czechoslovak Math. J. 45, 107–116 (1995)MathSciNetMATH F.S. De Blasi, G. Pianigiani, V. Staicu: On the solution sets of some nonconvex hyperbolic differential inclusions. Czechoslovak Math. J. 45, 107–116 (1995)MathSciNetMATH
81.
Zurück zum Zitat H.F. Bohnenblust, S. Karlin, On a theorem of ville. Contribution to the theory of games, in Annals of Mathematics Studies, vol. 24 (Priceton University Press, Princeton. N. G., 1950), pp. 155–160 H.F. Bohnenblust, S. Karlin, On a theorem of ville. Contribution to the theory of games, in Annals of Mathematics Studies, vol. 24 (Priceton University Press, Princeton. N. G., 1950), pp. 155–160
82.
Zurück zum Zitat A. Bressan, G. Colombo, Extensions and selections of maps with decomposable values. Studia Math. 90, 69–86 (1988)MathSciNetMATH A. Bressan, G. Colombo, Extensions and selections of maps with decomposable values. Studia Math. 90, 69–86 (1988)MathSciNetMATH
85.
Zurück zum Zitat L. Byszewski, Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation u xt  = F(x, t, u, u x ). J. Appl. Math. Stochastic Anal. 3, 163–168 (1990)MathSciNetCrossRefMATH L. Byszewski, Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation u xt  = F(x, t, u, u x ). J. Appl. Math. Stochastic Anal. 3, 163–168 (1990)MathSciNetCrossRefMATH
86.
Zurück zum Zitat L. Byszewski, Theorem about existence and uniqueness of continuous solutions of nonlocal problem for nonlinear hyperbolic equation. Appl. Anal. 40, 173–180 (1991)MathSciNetCrossRefMATH L. Byszewski, Theorem about existence and uniqueness of continuous solutions of nonlocal problem for nonlinear hyperbolic equation. Appl. Anal. 40, 173–180 (1991)MathSciNetCrossRefMATH
87.
Zurück zum Zitat L. Byszewski, Existence and uniqueness of mild and classical solutions of semilinear functional differential evolution nonlocal Cauchy problem, Selected Problems in Mathematics, Cracow Univ. of Tech. Monographs, Anniversary Issue 6, 25–33 (1995) L. Byszewski, Existence and uniqueness of mild and classical solutions of semilinear functional differential evolution nonlocal Cauchy problem, Selected Problems in Mathematics, Cracow Univ. of Tech. Monographs, Anniversary Issue 6, 25–33 (1995)
88.
Zurück zum Zitat L. Byszewski, V. Lakshmikantam, Monotone iterative technique for non-local hyperbolic differential problem. J. Math. Phys. Sci 26, 345–359 (1992)MathSciNetMATH L. Byszewski, V. Lakshmikantam, Monotone iterative technique for non-local hyperbolic differential problem. J. Math. Phys. Sci 26, 345–359 (1992)MathSciNetMATH
89.
Zurück zum Zitat L. Byszewski, S.N. Papageorgiou, An application of a noncompactness technique to an investigation of the existence of solutions to a nonlocal multivalued Darboux problem. J. Appl. Math. Stoch. Anal. 12, 179–180 (1999)MathSciNetCrossRefMATH L. Byszewski, S.N. Papageorgiou, An application of a noncompactness technique to an investigation of the existence of solutions to a nonlocal multivalued Darboux problem. J. Appl. Math. Stoch. Anal. 12, 179–180 (1999)MathSciNetCrossRefMATH
90.
Zurück zum Zitat M. Caputo, Linear models of dissipation whose Q is almost frequency independent II. Geophys. J. Roy. Astron. Soc. 13, 529–539 (1967), reprinted in Fract. Calc. Appl. Anal. 11, 4–14 (2008) M. Caputo, Linear models of dissipation whose Q is almost frequency independent II. Geophys. J. Roy. Astron. Soc. 13, 529–539 (1967), reprinted in Fract. Calc. Appl. Anal. 11, 4–14 (2008)
91.
Zurück zum Zitat M. Caputo, Linear models of dissipation whose ℚ is almost frequency independent-II. Geophys. J. R. Astr. Soc. 13, 529–539 (1967)CrossRef M. Caputo, Linear models of dissipation whose is almost frequency independent-II. Geophys. J. R. Astr. Soc. 13, 529–539 (1967)CrossRef
92.
Zurück zum Zitat M. Caputo, in Elasticità e Dissipazione (Zanichelli, Bologna, 1969) M. Caputo, in Elasticità e Dissipazione (Zanichelli, Bologna, 1969)
93.
Zurück zum Zitat C. Castaing, M. Valadier, in Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, vol. 580 (Springer, Berlin, 1977) C. Castaing, M. Valadier, in Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, vol. 580 (Springer, Berlin, 1977)
94.
Zurück zum Zitat Y.-K. Chang, J.J. Nieto, Some new existence results for fractional differential inclusions with boundary conditions. Math. Comput. Model. 49, 605–609 (2009)MathSciNetCrossRefMATH Y.-K. Chang, J.J. Nieto, Some new existence results for fractional differential inclusions with boundary conditions. Math. Comput. Model. 49, 605–609 (2009)MathSciNetCrossRefMATH
95.
Zurück zum Zitat C. Corduneanu, in Integral Equations and Applications (Cambridge University Press, Cambridge, 1991) C. Corduneanu, in Integral Equations and Applications (Cambridge University Press, Cambridge, 1991)
96.
97.
Zurück zum Zitat T. Czlapinski, On the Darboux problem for partial differential-functional equations with infinite delay at derivatives. Nonlinear Anal. 44, 389–398 (2001)MathSciNetCrossRefMATH T. Czlapinski, On the Darboux problem for partial differential-functional equations with infinite delay at derivatives. Nonlinear Anal. 44, 389–398 (2001)MathSciNetCrossRefMATH
98.
Zurück zum Zitat T. Czlapinski, Existence of solutions of the Darboux problem for partial differential-functional equations with infinite delay in a Banach space. Comment. Math. Prace Mat. 35, 111–122 (1995)MathSciNetMATH T. Czlapinski, Existence of solutions of the Darboux problem for partial differential-functional equations with infinite delay in a Banach space. Comment. Math. Prace Mat. 35, 111–122 (1995)MathSciNetMATH
99.
Zurück zum Zitat M.F. Danca, K. Diethelm, Kai. Fractional-order attractors synthesis via parameter switchings. Commun. Nonlinear Sci. Numer. Simul. 15(12), 3745–3753 (2010)MathSciNetMATH M.F. Danca, K. Diethelm, Kai. Fractional-order attractors synthesis via parameter switchings. Commun. Nonlinear Sci. Numer. Simul. 15(12), 3745–3753 (2010)MathSciNetMATH
100.
Zurück zum Zitat M.A. Darwish, J. Henderson, D. O’Regan, Existence and asymptotic stability of solutions of a perturbed fractional functional-integral equation with linear modification of the argument. Bull. Korean Math. Soc. 48, 539–553 (2011)MathSciNetCrossRefMATH M.A. Darwish, J. Henderson, D. O’Regan, Existence and asymptotic stability of solutions of a perturbed fractional functional-integral equation with linear modification of the argument. Bull. Korean Math. Soc. 48, 539–553 (2011)MathSciNetCrossRefMATH
101.
Zurück zum Zitat M. Dawidowski, I. Kubiaczyk, An existence theorem for the generalized hyperbolic equation z′ xy  ∈ F(x, y, z) in Banach space. Ann. Soc. Math. Pol. Ser. I Comment. Math. 30(1), 41–49 (1990)MathSciNetMATH M. Dawidowski, I. Kubiaczyk, An existence theorem for the generalized hyperbolic equation z′ xy  ∈ F(x, y, z) in Banach space. Ann. Soc. Math. Pol. Ser. I Comment. Math. 30(1), 41–49 (1990)MathSciNetMATH
102.
Zurück zum Zitat A. Debbouche, Fractional evolution integro-differential systems with nonlocal conditions. Adv. Dyn. Syst. Appl. 5(1), 49–60 (2010)MathSciNet A. Debbouche, Fractional evolution integro-differential systems with nonlocal conditions. Adv. Dyn. Syst. Appl. 5(1), 49–60 (2010)MathSciNet
103.
Zurück zum Zitat A. Debbouche, D. Baleanu, Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems. Comput. Math. Appl. 62, 1442–1450 (2011)MathSciNetCrossRefMATH A. Debbouche, D. Baleanu, Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems. Comput. Math. Appl. 62, 1442–1450 (2011)MathSciNetCrossRefMATH
104.
Zurück zum Zitat K. Deimling, in Multivalued Differential Equations (Walter De Gruyter, Berlin, 1992)MATH K. Deimling, in Multivalued Differential Equations (Walter De Gruyter, Berlin, 1992)MATH
105.
Zurück zum Zitat D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation. J. Math. Anal. Appl. 204, 609–625 (1996)MathSciNetCrossRefMATH D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation. J. Math. Anal. Appl. 204, 609–625 (1996)MathSciNetCrossRefMATH
106.
Zurück zum Zitat Z. Denton, A.S. Vatsala, Monotone iterative technique for finite systems of nonlinear Riemann-Liouville fractional differential equations. Opuscula Math. 31(3), 327–339 (2011)MathSciNetMATH Z. Denton, A.S. Vatsala, Monotone iterative technique for finite systems of nonlinear Riemann-Liouville fractional differential equations. Opuscula Math. 31(3), 327–339 (2011)MathSciNetMATH
107.
Zurück zum Zitat B.C. Dhage, A nonlinear alternative in Banach algebras with applications to functional differential equations. Nonlinear Funct. Anal. Appl. 8, 563–575 (2004)MathSciNet B.C. Dhage, A nonlinear alternative in Banach algebras with applications to functional differential equations. Nonlinear Funct. Anal. Appl. 8, 563–575 (2004)MathSciNet
108.
Zurück zum Zitat B.C. Dhage, Some algebraic fixed point theorems for multi-valued mappings with applications. Diss. Math. Differ. Inclusions Contr. Optim. 26, 5–55 (2006)MathSciNetCrossRefMATH B.C. Dhage, Some algebraic fixed point theorems for multi-valued mappings with applications. Diss. Math. Differ. Inclusions Contr. Optim. 26, 5–55 (2006)MathSciNetCrossRefMATH
109.
Zurück zum Zitat B.C. Dhage, Nonlinear functional boundary value problems in Banach algebras involving Carathéodories. Kyungpook Math. J. 46(4), 527–541 (2006)MathSciNetMATH B.C. Dhage, Nonlinear functional boundary value problems in Banach algebras involving Carathéodories. Kyungpook Math. J. 46(4), 527–541 (2006)MathSciNetMATH
110.
Zurück zum Zitat B.C. Dhage, Existence theorems for hyperbolic differential inclusions in Banach algebras. J. Math. Anal. Appl. 335, 225–242 (2007)MathSciNetCrossRefMATH B.C. Dhage, Existence theorems for hyperbolic differential inclusions in Banach algebras. J. Math. Anal. Appl. 335, 225–242 (2007)MathSciNetCrossRefMATH
111.
Zurück zum Zitat B.C. Dhage, Attractivity and positivity results for nonlinear functional integral equations via measure of noncompactness. Diff. Equ. Appl. 2(3), 299–318 (2010)MathSciNetMATH B.C. Dhage, Attractivity and positivity results for nonlinear functional integral equations via measure of noncompactness. Diff. Equ. Appl. 2(3), 299–318 (2010)MathSciNetMATH
112.
Zurück zum Zitat T. Diagana, G.M. Mophou, G.M. N’Guérékata, On the existence of mild solutions to some semilinear fractional integro-differential equations. Electron. J. Qual. Theory Differ. Equ. 2010 (58), 17 T. Diagana, G.M. Mophou, G.M. N’Guérékata, On the existence of mild solutions to some semilinear fractional integro-differential equations. Electron. J. Qual. Theory Differ. Equ. 2010 (58), 17
113.
Zurück zum Zitat K. Diethelm, in The Analysis of Fractional Differential Equations. Lecture Notes in Mathematics (Springer, Berlin, 2010) K. Diethelm, in The Analysis of Fractional Differential Equations. Lecture Notes in Mathematics (Springer, Berlin, 2010)
114.
115.
Zurück zum Zitat K. Diethelm, A.D. Freed, On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity, in Scientifice Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties, ed. by F. Keil, W. Mackens, H. Voss, J. Werther (Springer, Heidelberg, 1999), pp. 217–224 K. Diethelm, A.D. Freed, On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity, in Scientifice Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties, ed. by F. Keil, W. Mackens, H. Voss, J. Werther (Springer, Heidelberg, 1999), pp. 217–224
116.
Zurück zum Zitat X. Dong, J. Wang, Y. Zhou, Yong. On nonlocal problems for fractional differential equations in Banach spaces. Opuscula Math. 31(3), 341–357 (2011)MathSciNetMATH X. Dong, J. Wang, Y. Zhou, Yong. On nonlocal problems for fractional differential equations in Banach spaces. Opuscula Math. 31(3), 341–357 (2011)MathSciNetMATH
117.
Zurück zum Zitat S. Dugowson, L’élaboration par Riemann d’une définition de la dérivation d’ordre non entier. revue d’histoire des Mathématiques 3, 49–97 (1997) S. Dugowson, L’élaboration par Riemann d’une définition de la dérivation d’ordre non entier. revue d’histoire des Mathématiques 3, 49–97 (1997)
118.
Zurück zum Zitat M.M. El-Borai, On some fractional evolution equations with nonlocal conditions. Int. J. Pure Appl. Math. 24, 405–413 (2005)MathSciNetMATH M.M. El-Borai, On some fractional evolution equations with nonlocal conditions. Int. J. Pure Appl. Math. 24, 405–413 (2005)MathSciNetMATH
119.
Zurück zum Zitat M.M. El-Borai, The fundamental solutions for fractional evolution equations of parabolic type. J. Appl. Math. Stoch. Anal. 2004(3), 197–211MathSciNetCrossRef M.M. El-Borai, The fundamental solutions for fractional evolution equations of parabolic type. J. Appl. Math. Stoch. Anal. 2004(3), 197–211MathSciNetCrossRef
120.
Zurück zum Zitat M.M. El-Borai, K. El-Said El-Nadi, E.G. El-Akabawy On some fractional evolution equations. Comput. Math. Appl. 59(3), 1352–1355 (2010)MathSciNetCrossRefMATH M.M. El-Borai, K. El-Said El-Nadi, E.G. El-Akabawy On some fractional evolution equations. Comput. Math. Appl. 59(3), 1352–1355 (2010)MathSciNetCrossRefMATH
121.
Zurück zum Zitat M.M. El-Borai, K. El-Nadi, H.A. Fouad, On some fractional stochastic delay differential equations. Comput. Math. Appl. 59(3), 1165–1170 (2010)MathSciNetCrossRefMATH M.M. El-Borai, K. El-Nadi, H.A. Fouad, On some fractional stochastic delay differential equations. Comput. Math. Appl. 59(3), 1165–1170 (2010)MathSciNetCrossRefMATH
122.
124.
125.
Zurück zum Zitat J.B.J. Fourier, Théorie Analytique de la Chaleur, Didot, Paris, 499–508 (1822) J.B.J. Fourier, Théorie Analytique de la Chaleur, Didot, Paris, 499–508 (1822)
126.
Zurück zum Zitat M. Frigon, Théorèmes d’existence de solutions d’inclusions différentielles, Topological Methods in Differential Equations and Inclusions, NATO ASI Series C, vol. 472, ed. by A. Granas, M. Frigon (Kluwer Academic Publishers, Dordrecht, 1995), pp. 51–87 M. Frigon, Théorèmes d’existence de solutions d’inclusions différentielles, Topological Methods in Differential Equations and Inclusions, NATO ASI Series C, vol. 472, ed. by A. Granas, M. Frigon (Kluwer Academic Publishers, Dordrecht, 1995), pp. 51–87
127.
Zurück zum Zitat M. Frigon, A. Granas, Théorèmes d’existence pour des inclusions différentielles sans convexité. C. R. Acad. Sci. Paris, Ser. I 310, 819–822 (1990) M. Frigon, A. Granas, Théorèmes d’existence pour des inclusions différentielles sans convexité. C. R. Acad. Sci. Paris, Ser. I 310, 819–822 (1990)
128.
129.
Zurück zum Zitat M. Frigon, D. O’Regan, First order impulsive initial and periodic problems with variable moments. J. Math. Anal. Appl. 233, 730–739 (1999)MathSciNetCrossRefMATH M. Frigon, D. O’Regan, First order impulsive initial and periodic problems with variable moments. J. Math. Anal. Appl. 233, 730–739 (1999)MathSciNetCrossRefMATH
130.
Zurück zum Zitat M. Frigon, D. O’Regan, Second order Sturm-Liouville BVP’s with impulses at variable moments. Dynam. Contin. Discrete Impuls. Syst. 8 (2), 149–159 (2001)MathSciNetMATH M. Frigon, D. O’Regan, Second order Sturm-Liouville BVP’s with impulses at variable moments. Dynam. Contin. Discrete Impuls. Syst. 8 (2), 149–159 (2001)MathSciNetMATH
131.
Zurück zum Zitat K.M. Furati, N.-eddine Tatar, Behavior of solutions for a weighted Cauchy-type fractional differential problem. J. Frac. Calc. 28, 23–42 (2005) K.M. Furati, N.-eddine Tatar, Behavior of solutions for a weighted Cauchy-type fractional differential problem. J. Frac. Calc. 28, 23–42 (2005)
132.
Zurück zum Zitat K.M. Furati, N.-eddine Tatar, Power type estimates for a nonlinear fractional differential equation. Nonlinear Anal. 62, 1025–1036 (2005) K.M. Furati, N.-eddine Tatar, Power type estimates for a nonlinear fractional differential equation. Nonlinear Anal. 62, 1025–1036 (2005)
133.
Zurück zum Zitat L. Gaul, P. Klein, S. Kempfle, Damping description involving fractional operators. Mech. Syst. Signal Process. 5, 81–88 (1991)CrossRef L. Gaul, P. Klein, S. Kempfle, Damping description involving fractional operators. Mech. Syst. Signal Process. 5, 81–88 (1991)CrossRef
134.
Zurück zum Zitat W.G. Glockle, T.F. Nonnenmacher, A fractional calculus approach of self-similar protein dynamics. Biophys. J. 68, 46–53 (1995)CrossRef W.G. Glockle, T.F. Nonnenmacher, A fractional calculus approach of self-similar protein dynamics. Biophys. J. 68, 46–53 (1995)CrossRef
135.
Zurück zum Zitat L. Gorniewicz, in Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, vol. 495 (Kluwer Academic Publishers, Dordrecht, 1999) L. Gorniewicz, in Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, vol. 495 (Kluwer Academic Publishers, Dordrecht, 1999)
136.
Zurück zum Zitat A. Granas, J. Dugundji, in Fixed Point Theory (Springer, New York, 2003) A. Granas, J. Dugundji, in Fixed Point Theory (Springer, New York, 2003)
137.
Zurück zum Zitat A.K. Grunwald, Dérivationen und deren Anwendung. Zeitschrift für Mathematik und Phisik, 12, 441–480 (1867) A.K. Grunwald, Dérivationen und deren Anwendung. Zeitschrift für Mathematik und Phisik, 12, 441–480 (1867)
138.
Zurück zum Zitat J. Hale, J. Kato, Phase space for retarded equationswith infinite delay. Funkcial. Ekvac. 21, 11–41 (1978)MathSciNetMATH J. Hale, J. Kato, Phase space for retarded equationswith infinite delay. Funkcial. Ekvac. 21, 11–41 (1978)MathSciNetMATH
139.
Zurück zum Zitat J.K. Hale, S. Verduyn Lunel, in Introduction to Functional -Differential Equations. Applied Mathematical Sciences, vol. 99 (Springer, New York, 1993) J.K. Hale, S. Verduyn Lunel, in Introduction to Functional -Differential Equations. Applied Mathematical Sciences, vol. 99 (Springer, New York, 1993)
140.
Zurück zum Zitat F. Hartung, Differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays. J. Math. Anal. Appl. 324(1), 504–524 (2006)MathSciNetCrossRefMATH F. Hartung, Differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays. J. Math. Anal. Appl. 324(1), 504–524 (2006)MathSciNetCrossRefMATH
141.
Zurück zum Zitat F. Hartung, Linearized stability in periodic functional differential equations with state-dependent delays. J. Comput. Appl. Math. 174(2), 201–211 (2005)MathSciNetCrossRefMATH F. Hartung, Linearized stability in periodic functional differential equations with state-dependent delays. J. Comput. Appl. Math. 174(2), 201–211 (2005)MathSciNetCrossRefMATH
142.
Zurück zum Zitat D. Henry, in Geometric Theory of Semilinear Parabolic Partial Differential Equations (Springer, Berlin, 1989) D. Henry, in Geometric Theory of Semilinear Parabolic Partial Differential Equations (Springer, Berlin, 1989)
143.
Zurück zum Zitat S. Heikkila, V. Lakshmikantham, in Monotone Iterative Technique for Nonlinear Discontinuous Differential Equations (Marcel Dekker Inc., New York, 1994) S. Heikkila, V. Lakshmikantham, in Monotone Iterative Technique for Nonlinear Discontinuous Differential Equations (Marcel Dekker Inc., New York, 1994)
144.
Zurück zum Zitat J. Henderson, A. Ouahab, Fractional functional differential inclusions with finite delay. Nonlinear Anal. 70 (2009) 2091–2105MathSciNetCrossRefMATH J. Henderson, A. Ouahab, Fractional functional differential inclusions with finite delay. Nonlinear Anal. 70 (2009) 2091–2105MathSciNetCrossRefMATH
145.
146.
Zurück zum Zitat J. Henderson, C. Tisdell, Topological transversality and boundary value problems on time scales. J. Math. Anal. Appl. 289, 110–125 (2004)MathSciNetCrossRefMATH J. Henderson, C. Tisdell, Topological transversality and boundary value problems on time scales. J. Math. Anal. Appl. 289, 110–125 (2004)MathSciNetCrossRefMATH
147.
Zurück zum Zitat E. Hernández, A. Prokopczyk, L. Ladeira, A note on partial functional differential equations with state-dependent delay. Nonlinear Anal. Real World Applications 7, 510–519 (2006)CrossRefMATH E. Hernández, A. Prokopczyk, L. Ladeira, A note on partial functional differential equations with state-dependent delay. Nonlinear Anal. Real World Applications 7, 510–519 (2006)CrossRefMATH
148.
Zurück zum Zitat E. Hernandez M., R. Sakthivel, S. Tanaka Aki, Existence results for impulsive evolution differential equations with state-dependent delay. Electron. J. Differ. Equat. 2008 (28), 1–11 (2008) E. Hernandez M., R. Sakthivel, S. Tanaka Aki, Existence results for impulsive evolution differential equations with state-dependent delay. Electron. J. Differ. Equat. 2008 (28), 1–11 (2008)
149.
Zurück zum Zitat M.A.E. Herzallah, D. Baleanu, Fractional-order variational calculus with generalized boundary conditions. Adv. Difference Equ. Article ID 357580, 9 p 2011 M.A.E. Herzallah, D. Baleanu, Fractional-order variational calculus with generalized boundary conditions. Adv. Difference Equ. Article ID 357580, 9 p 2011
150.
Zurück zum Zitat M.A.E. Herzallah, A.M.A. El-Sayed, D. Baleanu, Perturbation for fractional-order evolution equation. Nonlinear Dynam. 62(3), 593–600 (2010)MathSciNetCrossRefMATH M.A.E. Herzallah, A.M.A. El-Sayed, D. Baleanu, Perturbation for fractional-order evolution equation. Nonlinear Dynam. 62(3), 593–600 (2010)MathSciNetCrossRefMATH
151.
Zurück zum Zitat R. Hilfer, in Applications of Fractional Calculus in Physics (World Scientific, Singapore, 2000)MATH R. Hilfer, in Applications of Fractional Calculus in Physics (World Scientific, Singapore, 2000)MATH
152.
Zurück zum Zitat Y. Hino, S. Murakami, T. Naito, in Functional Differential Equations with Infinite Delay. Lecture Notes in Mathematics, vol. 1473 (Springer, Berlin, 1991) Y. Hino, S. Murakami, T. Naito, in Functional Differential Equations with Infinite Delay. Lecture Notes in Mathematics, vol. 1473 (Springer, Berlin, 1991)
153.
Zurück zum Zitat Sh. Hu, N. Papageorgiou, in Handbook of Multivalued Analysis, Theory I (Kluwer, Dordrecht, 1997)MATH Sh. Hu, N. Papageorgiou, in Handbook of Multivalued Analysis, Theory I (Kluwer, Dordrecht, 1997)MATH
154.
Zurück zum Zitat R.W. Ibrahim, Existence and uniqueness of holomorphic solutions for fractional Cauchy problem. J. Math. Anal. Appl. 380, 232–240 (2011)MathSciNetCrossRefMATH R.W. Ibrahim, Existence and uniqueness of holomorphic solutions for fractional Cauchy problem. J. Math. Anal. Appl. 380, 232–240 (2011)MathSciNetCrossRefMATH
155.
Zurück zum Zitat R.W. Ibrahim, H.A. Jalab, Existence of the solution of fractiona integral inclusion with time delay. Misk. Math. Notes 11(2), 139–150 (2010)MathSciNetMATH R.W. Ibrahim, H.A. Jalab, Existence of the solution of fractiona integral inclusion with time delay. Misk. Math. Notes 11(2), 139–150 (2010)MathSciNetMATH
156.
Zurück zum Zitat T. Kaczorek, in Selected Problems of Fractional Systems Theory (Springer, London, 2011) T. Kaczorek, in Selected Problems of Fractional Systems Theory (Springer, London, 2011)
157.
Zurück zum Zitat A. Kadem, D. Baleanu, Homotopy perturbation method for the coupled fractional Lotka-Volterra equations. Romanian J. Phys. 56(3–4), 332–338 (2011)MathSciNetMATH A. Kadem, D. Baleanu, Homotopy perturbation method for the coupled fractional Lotka-Volterra equations. Romanian J. Phys. 56(3–4), 332–338 (2011)MathSciNetMATH
158.
Zurück zum Zitat Z. Kamont, in Hyperbolic Functional Differential Inequalities and Applications (Kluwer Academic Publishers, Dordrecht, 1999) Z. Kamont, in Hyperbolic Functional Differential Inequalities and Applications (Kluwer Academic Publishers, Dordrecht, 1999)
159.
Zurück zum Zitat Z. Kamont, K. Kropielnicka, Differential difference inequalities related to hyperbolic functional differential systems and applications. Math. Inequal. Appl. 8(4), 655–674 (2005)MathSciNetMATH Z. Kamont, K. Kropielnicka, Differential difference inequalities related to hyperbolic functional differential systems and applications. Math. Inequal. Appl. 8(4), 655–674 (2005)MathSciNetMATH
160.
Zurück zum Zitat S.K. Kaul, V. Lakshmikantham, S. Leela, Extremal solutions, comparison principle and stability criteria for impulsive differential equations with variable times. Nonlinear Anal. 22, 1263–1270 (1994)MathSciNetCrossRefMATH S.K. Kaul, V. Lakshmikantham, S. Leela, Extremal solutions, comparison principle and stability criteria for impulsive differential equations with variable times. Nonlinear Anal. 22, 1263–1270 (1994)MathSciNetCrossRefMATH
161.
Zurück zum Zitat S.K. Kaul, X.Z. Liu, Vector Lyapunov functions for impulsive differential systems with variable times. Dynam. Contin. Discrete Impuls. Syst. 6, 25–38 (1999)MathSciNetMATH S.K. Kaul, X.Z. Liu, Vector Lyapunov functions for impulsive differential systems with variable times. Dynam. Contin. Discrete Impuls. Syst. 6, 25–38 (1999)MathSciNetMATH
162.
Zurück zum Zitat S.K. Kaul, X.Z. Liu, Impulsive integro-differential equations with variable times. Nonlinear Stud. 8, 21–32 (2001)MathSciNetMATH S.K. Kaul, X.Z. Liu, Impulsive integro-differential equations with variable times. Nonlinear Stud. 8, 21–32 (2001)MathSciNetMATH
163.
Zurück zum Zitat E.R. Kaufmann, E. Mboumi, Positive solutions of a boundary value problem for a nonlinear fractional differential equation. Electron. J. Qual. Theory Differ. Equat. (3), 11 (2007) E.R. Kaufmann, E. Mboumi, Positive solutions of a boundary value problem for a nonlinear fractional differential equation. Electron. J. Qual. Theory Differ. Equat. (3), 11 (2007)
164.
Zurück zum Zitat A.A. Kilbas, B. Bonilla, J. Trujillo, Nonlinear differential equations of fractional order in a space of integrable functions. Dokl. Ross. Akad. Nauk 374(4), 445–449 (2000)MathSciNet A.A. Kilbas, B. Bonilla, J. Trujillo, Nonlinear differential equations of fractional order in a space of integrable functions. Dokl. Ross. Akad. Nauk 374(4), 445–449 (2000)MathSciNet
165.
Zurück zum Zitat A.A. Kilbas, S.A. Marzan, Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions. Differ. Equat. 41, 84–89 (2005)MathSciNetCrossRefMATH A.A. Kilbas, S.A. Marzan, Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions. Differ. Equat. 41, 84–89 (2005)MathSciNetCrossRefMATH
166.
Zurück zum Zitat A.A. Kilbas, Hari M. Srivastava, and Juan J. Trujillo, in Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204 (Elsevier Science B.V., Amsterdam, 2006) A.A. Kilbas, Hari M. Srivastava, and Juan J. Trujillo, in Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204 (Elsevier Science B.V., Amsterdam, 2006)
167.
Zurück zum Zitat M. Kirane, M. Medved, N. Tatar, Semilinear Volterra integrodifferential problems with fractional derivatives in the nonlinearities. Abstr. Appl. Anal. 2011, Art. ID 510314, 11 pp M. Kirane, M. Medved, N. Tatar, Semilinear Volterra integrodifferential problems with fractional derivatives in the nonlinearities. Abstr. Appl. Anal. 2011, Art. ID 510314, 11 pp
168.
Zurück zum Zitat V.S. Kiryakova, Y.F. Luchko, The multi-index Mittag-Leffler functions and their appplications for solving fractional order problems in applied analysis. Application of mathematics in technical and natural sciences, 597–613, AIP Conf. Proc., 1301, Amer. Inst. Phys., Melville, NY, 2010 V.S. Kiryakova, Y.F. Luchko, The multi-index Mittag-Leffler functions and their appplications for solving fractional order problems in applied analysis. Application of mathematics in technical and natural sciences, 597–613, AIP Conf. Proc., 1301, Amer. Inst. Phys., Melville, NY, 2010
169.
Zurück zum Zitat M. Kisielewicz, in Differential Inclusions and Optimal Control (Kluwer, Dordrecht, The Netherlands, 1991) M. Kisielewicz, in Differential Inclusions and Optimal Control (Kluwer, Dordrecht, The Netherlands, 1991)
170.
Zurück zum Zitat S. Labidi, N. Tatar, Blow-up of solutions for a nonlinear beam equation with fractional feedback. Nonlinear Anal. 74(4), 1402–1409 (2011)MathSciNetCrossRefMATH S. Labidi, N. Tatar, Blow-up of solutions for a nonlinear beam equation with fractional feedback. Nonlinear Anal. 74(4), 1402–1409 (2011)MathSciNetCrossRefMATH
171.
Zurück zum Zitat S.F. Lacroix, Traité du Calcul Différentiel et du Calcul Intégral, Courcier, Paris, t.3 (1819), 409–410 S.F. Lacroix, Traité du Calcul Différentiel et du Calcul Intégral, Courcier, Paris, t.3 (1819), 409–410
172.
Zurück zum Zitat G.S. Ladde, V. Lakshmikanthan, A.S. Vatsala, in Monotone Iterative Techniques for Nonliner Differential Equations (Pitman Advanced Publishing Program, London, 1985) G.S. Ladde, V. Lakshmikanthan, A.S. Vatsala, in Monotone Iterative Techniques for Nonliner Differential Equations (Pitman Advanced Publishing Program, London, 1985)
173.
174.
Zurück zum Zitat V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, in Theory of Impulsive Differential Equations (World Scientific, Singapore, 1989) V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, in Theory of Impulsive Differential Equations (World Scientific, Singapore, 1989)
175.
Zurück zum Zitat V. Lakshmikantham, S. Leela, J. Vasundhara, in Theory of Fractional Dynamic Systems (Cambridge Academic Publishers, Cambridge, 2009) V. Lakshmikantham, S. Leela, J. Vasundhara, in Theory of Fractional Dynamic Systems (Cambridge Academic Publishers, Cambridge, 2009)
176.
Zurück zum Zitat V. Lakshmikantham, S.G. Pandit, The method of upper, lower solutions and hyperbolic partial differential equations. J. Math. Anal. Appl. 105, 466–477 (1985)MathSciNetCrossRefMATH V. Lakshmikantham, S.G. Pandit, The method of upper, lower solutions and hyperbolic partial differential equations. J. Math. Anal. Appl. 105, 466–477 (1985)MathSciNetCrossRefMATH
177.
Zurück zum Zitat V. Lakshmikantham, N.S. Papageorgiou, J. Vasundhara, The method of upper and lower solutions and monotone technique for impulsive differential equations with variable moments. Appl. Anal. 15, 41–58 (1993)MathSciNetCrossRef V. Lakshmikantham, N.S. Papageorgiou, J. Vasundhara, The method of upper and lower solutions and monotone technique for impulsive differential equations with variable moments. Appl. Anal. 15, 41–58 (1993)MathSciNetCrossRef
178.
179.
Zurück zum Zitat V. Lakshmikantham, L. Wen, B. Zhang, in Theory of Differential Equations with Unbounded Delay. Mathematics and its Applications (Kluwer Academic Publishers, Dordrecht, 1994) V. Lakshmikantham, L. Wen, B. Zhang, in Theory of Differential Equations with Unbounded Delay. Mathematics and its Applications (Kluwer Academic Publishers, Dordrecht, 1994)
180.
Zurück zum Zitat A. Lasota, Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13, 781–786 (1965)MathSciNetMATH A. Lasota, Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13, 781–786 (1965)MathSciNetMATH
181.
Zurück zum Zitat G.W. Leibniz, Letter from Hanover, Germany, Deptember 30, 1695 to G.A. L’Hospital, in JLeibnizen Mathematische Schriften, vol. 2 (Olms Verlag, Hildesheim, Germany, 1962), pp. 301–302. First published in 1849 G.W. Leibniz, Letter from Hanover, Germany, Deptember 30, 1695 to G.A. L’Hospital, in JLeibnizen Mathematische Schriften, vol. 2 (Olms Verlag, Hildesheim, Germany, 1962), pp. 301–302. First published in 1849
182.
Zurück zum Zitat F. Li, G.M. N’Guérékata, An existence result for neutral delay integrodifferential equations with fractional order and nonlocal conditions Abst. Appl. Anal. (2011), Article ID 952782, 20 pages F. Li, G.M. N’Guérékata, An existence result for neutral delay integrodifferential equations with fractional order and nonlocal conditions Abst. Appl. Anal. (2011), Article ID 952782, 20 pages
183.
Zurück zum Zitat Y. Li, Y. Chen, I. Podlubny, Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput. Math. Appl. 59(5), 1810–1821 (2010)MathSciNetCrossRefMATH Y. Li, Y. Chen, I. Podlubny, Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput. Math. Appl. 59(5), 1810–1821 (2010)MathSciNetCrossRefMATH
184.
Zurück zum Zitat T.C. Lim, On fixed point stability for set-valued contractive mappings with applications to generalized differential equations. J. Math. Anal. Appl. 110, 436–441 (1985)MathSciNetCrossRefMATH T.C. Lim, On fixed point stability for set-valued contractive mappings with applications to generalized differential equations. J. Math. Anal. Appl. 110, 436–441 (1985)MathSciNetCrossRefMATH
185.
Zurück zum Zitat J. Liouville, Mémoire sur le calcul des différentielles à indices quelconques. J. l’Ecole Roy. Polytéchn. 13, 529–539 (1832) J. Liouville, Mémoire sur le calcul des différentielles à indices quelconques. J. l’Ecole Roy. Polytéchn. 13, 529–539 (1832)
186.
Zurück zum Zitat Y. Luchko, Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation. J. Math. Anal. Appl. 374, 538–548 (2011)MathSciNetCrossRefMATH Y. Luchko, Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation. J. Math. Anal. Appl. 374, 538–548 (2011)MathSciNetCrossRefMATH
187.
Zurück zum Zitat R. Magin, in Fractional Calculus in Bioengineering (Begell House Publishers, Redding, 2006) R. Magin, in Fractional Calculus in Bioengineering (Begell House Publishers, Redding, 2006)
188.
Zurück zum Zitat R. Magin, M.D. Ortigueira, I. Podlubny, J.J. Trujillo, On the fractional signals and systems. Signal Process. 91, 350–371 (2011)CrossRefMATH R. Magin, M.D. Ortigueira, I. Podlubny, J.J. Trujillo, On the fractional signals and systems. Signal Process. 91, 350–371 (2011)CrossRefMATH
189.
Zurück zum Zitat F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, in Fractals and Fractional Calculus in Continuum Mechanics ed. by A. Carpinteri, F. Mainardi (Springer-Verlag, Wien, 1997), pp. 291–348 F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, in Fractals and Fractional Calculus in Continuum Mechanics ed. by A. Carpinteri, F. Mainardi (Springer-Verlag, Wien, 1997), pp. 291–348
190.
Zurück zum Zitat S. Marano, V. Staicu, On the set of solutions to a class of nonconvex nonclosed differential inclusions. Acta Math. Hungar. 76, 287–301 (1997)MathSciNetCrossRefMATH S. Marano, V. Staicu, On the set of solutions to a class of nonconvex nonclosed differential inclusions. Acta Math. Hungar. 76, 287–301 (1997)MathSciNetCrossRefMATH
191.
Zurück zum Zitat F. Metzler, W. Schick, H.G. Kilian, T.F. Nonnenmacher, Relaxation in filled polymers: A fractional calculus approach. J. Chem. Phys. 103, 7180–7186 (1995)CrossRef F. Metzler, W. Schick, H.G. Kilian, T.F. Nonnenmacher, Relaxation in filled polymers: A fractional calculus approach. J. Chem. Phys. 103, 7180–7186 (1995)CrossRef
192.
Zurück zum Zitat K.S. Miller, B. Ross, in An Introduction to the Fractional Calculus and Differential Equations (Wiley, New York, 1993) K.S. Miller, B. Ross, in An Introduction to the Fractional Calculus and Differential Equations (Wiley, New York, 1993)
193.
Zurück zum Zitat V.D. Milman, A.A. Myshkis, On the stability of motion in the presence of impulses. Sib. Math. J. 1, 233–237 (1960), [in Russian] V.D. Milman, A.A. Myshkis, On the stability of motion in the presence of impulses. Sib. Math. J. 1, 233–237 (1960), [in Russian]
194.
Zurück zum Zitat V.D. Milman, A.A. Myshkis, Random impulses in linear dynamical systems, in Approximante Methods for Solving Differential Equations (Publishing House of the Academy of Sciences of Ukainian SSR, Kiev, 1963), pp. 64–81, [in Russian] V.D. Milman, A.A. Myshkis, Random impulses in linear dynamical systems, in Approximante Methods for Solving Differential Equations (Publishing House of the Academy of Sciences of Ukainian SSR, Kiev, 1963), pp. 64–81, [in Russian]
195.
Zurück zum Zitat G.M. Mittag-Leffler, Sur la nouvelle function E α. C. R. Acad. Sci. Paris 137, 554–558 (1903) G.M. Mittag-Leffler, Sur la nouvelle function E α. C. R. Acad. Sci. Paris 137, 554–558 (1903)
196.
Zurück zum Zitat G.M. Mittag-Leffler, Sopra la funzione E α(x). Rend. Accad. Lincei, ser. 5 13, 3–5 (1904) G.M. Mittag-Leffler, Sopra la funzione E α(x). Rend. Accad. Lincei, ser. 5 13, 3–5 (1904)
197.
Zurück zum Zitat K. Moaddy, S. Momani, I. Hashim, The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics. Comput. Math. Appl. 61(4), 1209–1216 (2011)MathSciNetCrossRefMATH K. Moaddy, S. Momani, I. Hashim, The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics. Comput. Math. Appl. 61(4), 1209–1216 (2011)MathSciNetCrossRefMATH
199.
Zurück zum Zitat M. Mophou, O. Nakoulima, G.M. N’Guérékata, Existence results for some fractional differential equations with nonlocal conditions. Nonlinear Stud. 17, 15–22 (2010)MathSciNetMATH M. Mophou, O. Nakoulima, G.M. N’Guérékata, Existence results for some fractional differential equations with nonlocal conditions. Nonlinear Stud. 17, 15–22 (2010)MathSciNetMATH
200.
Zurück zum Zitat G.M. Mophou, G.M. N’Guérékata, Existence of the mild solution for some fractional differential equations with nonlocal conditions. Semigroup Forum 79, 315–322 (2009)MathSciNetCrossRefMATH G.M. Mophou, G.M. N’Guérékata, Existence of the mild solution for some fractional differential equations with nonlocal conditions. Semigroup Forum 79, 315–322 (2009)MathSciNetCrossRefMATH
201.
Zurück zum Zitat G.M. Mophou, G.M. N’Guérékata, On some classes of almost automorphic functions and applications to fractional differential equations. Comput. Math. Appl. 59, 1310–1317 (2010)MathSciNetCrossRefMATH G.M. Mophou, G.M. N’Guérékata, On some classes of almost automorphic functions and applications to fractional differential equations. Comput. Math. Appl. 59, 1310–1317 (2010)MathSciNetCrossRefMATH
202.
Zurück zum Zitat G.M. Mophou, G.M. N’Guérékata, On integral solutions of some nonlocal fractional differential equations with nondense domain. Nonlinear Anal. 71, 4668–4675 (2009)MathSciNetCrossRefMATH G.M. Mophou, G.M. N’Guérékata, On integral solutions of some nonlocal fractional differential equations with nondense domain. Nonlinear Anal. 71, 4668–4675 (2009)MathSciNetCrossRefMATH
203.
Zurück zum Zitat G.M. Mophou, G.N. N’Guérékata, Controllability of semilinear neutral fractional functional evolution equations with infinite delay. Nonlinear Stud. 18, 195–209 (2011)MathSciNetMATH G.M. Mophou, G.N. N’Guérékata, Controllability of semilinear neutral fractional functional evolution equations with infinite delay. Nonlinear Stud. 18, 195–209 (2011)MathSciNetMATH
204.
Zurück zum Zitat G.M. Mophou, G.M. N’Guérékata, V. Valmorin, Pseudo almost automorphic solutions of a neutral functional fractional differential equations. Intern. J. Evol. Equ. 4, 129–139 (2009) G.M. Mophou, G.M. N’Guérékata, V. Valmorin, Pseudo almost automorphic solutions of a neutral functional fractional differential equations. Intern. J. Evol. Equ. 4, 129–139 (2009)
205.
Zurück zum Zitat S. Muslih, O.P. Agrawal, Riesz fractional derivatives and fractional dimensional space. Int. J. Theor. Phys. 49(2), 270–275 (2010)MathSciNetCrossRefMATH S. Muslih, O.P. Agrawal, Riesz fractional derivatives and fractional dimensional space. Int. J. Theor. Phys. 49(2), 270–275 (2010)MathSciNetCrossRefMATH
206.
Zurück zum Zitat S. Muslih, O.P. Agrawal, D. Baleanu, A fractional Schrdinger equation and its solution. Int. J. Theor. Phys. 49(8), 1746–1752 (2010)MathSciNetCrossRefMATH S. Muslih, O.P. Agrawal, D. Baleanu, A fractional Schrdinger equation and its solution. Int. J. Theor. Phys. 49(8), 1746–1752 (2010)MathSciNetCrossRefMATH
207.
Zurück zum Zitat J.J. Nieto, Maximum principles for fractional differential equations derived from Mittag-Leffler functions. Appl. Math. Lett. 23, 1248–1251 (2010)MathSciNetCrossRefMATH J.J. Nieto, Maximum principles for fractional differential equations derived from Mittag-Leffler functions. Appl. Math. Lett. 23, 1248–1251 (2010)MathSciNetCrossRefMATH
208.
Zurück zum Zitat K.B. Oldham, J. Spanier, in The Fractional Calculus (Academic Press, New York, 1974) K.B. Oldham, J. Spanier, in The Fractional Calculus (Academic Press, New York, 1974)
209.
Zurück zum Zitat M.D. Ortigueira, in Fractional Calculus for Scientists and Engineers (Springer, Dordrecht, 2011) M.D. Ortigueira, in Fractional Calculus for Scientists and Engineers (Springer, Dordrecht, 2011)
210.
Zurück zum Zitat B.G. Pachpatte, On Volterra-Fredholm integral equation in two variables. Demonstratio Math. XL(4), 839–852 (2007) B.G. Pachpatte, On Volterra-Fredholm integral equation in two variables. Demonstratio Math. XL(4), 839–852 (2007)
211.
Zurück zum Zitat B.G. Pachpatte, On Fredholm type integrodifferential equation. Tamkang J. Math. 39(1), 85–94 (2008)MathSciNetMATH B.G. Pachpatte, On Fredholm type integrodifferential equation. Tamkang J. Math. 39(1), 85–94 (2008)MathSciNetMATH
212.
Zurück zum Zitat B.G. Pachpatte, On Fredholm type integral equation in two variables. Diff. Equ. Appl. 1, 27–39 (2009)MATH B.G. Pachpatte, On Fredholm type integral equation in two variables. Diff. Equ. Appl. 1, 27–39 (2009)MATH
213.
Zurück zum Zitat S.G. Pandit, Monotone methods for systems of nonlinear hyperbolic problems in two independent variables. Nonlinear Anal. 30, 235–272 (1997)MathSciNetCrossRef S.G. Pandit, Monotone methods for systems of nonlinear hyperbolic problems in two independent variables. Nonlinear Anal. 30, 235–272 (1997)MathSciNetCrossRef
214.
Zurück zum Zitat I. Podlubny, in Fractional Differential Equations. Mathematics in Science and Engineering, vol. 198 (Academic Press, San Diego, 1999) I. Podlubny, in Fractional Differential Equations. Mathematics in Science and Engineering, vol. 198 (Academic Press, San Diego, 1999)
215.
Zurück zum Zitat I. Podlubny, Geometric and physical interpretation of fractional integration and fractional differentiation. Fract. Calculus Appl. Anal. 5, 367–386 (2002)MathSciNetMATH I. Podlubny, Geometric and physical interpretation of fractional integration and fractional differentiation. Fract. Calculus Appl. Anal. 5, 367–386 (2002)MathSciNetMATH
216.
Zurück zum Zitat I. Podlubny, I. Petraš, B.M. Vinagre, P. O’Leary, L. Dorčak, Analogue realizations of fractional-order controllers. Fractional order calculus and its applications. Nonlinear Dynam. 29, 281–296 (2002)MATH I. Podlubny, I. Petraš, B.M. Vinagre, P. O’Leary, L. Dorčak, Analogue realizations of fractional-order controllers. Fractional order calculus and its applications. Nonlinear Dynam. 29, 281–296 (2002)MATH
217.
Zurück zum Zitat J.D. Ramrez, A.S. Vatsala, Monotone method for nonlinear Caputo fractional boundary value problems. Dynam. Systems Appl. 20(1), 73–88 (2011)MathSciNet J.D. Ramrez, A.S. Vatsala, Monotone method for nonlinear Caputo fractional boundary value problems. Dynam. Systems Appl. 20(1), 73–88 (2011)MathSciNet
218.
Zurück zum Zitat A. Razminia, V.J. Majd, D. Baleanu, Chaotic incommensurate fractional order Rssler system: Active control and synchronization. Adv. Difference Equat. 2011(15), 12 (2011) A. Razminia, V.J. Majd, D. Baleanu, Chaotic incommensurate fractional order Rssler system: Active control and synchronization. Adv. Difference Equat. 2011(15), 12 (2011)
219.
Zurück zum Zitat M. Rivero, J.J. Trujillo, L. Vzquez, M.P. Velasco, Fractional dynamics of populations. Appl. Math. Comput. 218, 1089–1095 (2011)MathSciNetCrossRefMATH M. Rivero, J.J. Trujillo, L. Vzquez, M.P. Velasco, Fractional dynamics of populations. Appl. Math. Comput. 218, 1089–1095 (2011)MathSciNetCrossRefMATH
220.
Zurück zum Zitat J. Sabatier, O. Agrawal, J. Machado (eds.), in Advances in Fractional Calculus. Theoretical Developments and Applications in Physics and Engineering (Springer, Dordrecht, 2007) J. Sabatier, O. Agrawal, J. Machado (eds.), in Advances in Fractional Calculus. Theoretical Developments and Applications in Physics and Engineering (Springer, Dordrecht, 2007)
221.
Zurück zum Zitat J. Sabatier, M. Merveillaut, R. Malti, A. Oustaloup, How to impose physically coherent initial conditions to a fractional system? Commun. Nonlinear Sci. Numer. Simul. 15(5), 1318–1326 (2010)MathSciNetCrossRefMATH J. Sabatier, M. Merveillaut, R. Malti, A. Oustaloup, How to impose physically coherent initial conditions to a fractional system? Commun. Nonlinear Sci. Numer. Simul. 15(5), 1318–1326 (2010)MathSciNetCrossRefMATH
222.
Zurück zum Zitat H.A.H. Salem, On the fractional order m-point boundary value problem in reflexive Banach spaces and weak topologies. Comput. Math. Appl. 224, 565–572 (2009)MathSciNetCrossRefMATH H.A.H. Salem, On the fractional order m-point boundary value problem in reflexive Banach spaces and weak topologies. Comput. Math. Appl. 224, 565–572 (2009)MathSciNetCrossRefMATH
223.
Zurück zum Zitat H.A.H. Salem, On the fractional calculus in abstract spaces and their applications to the Dirichlet-type problem of fractional order. Comput. Math. Appl. 59(3), 1278–1293 (2010)MathSciNetCrossRefMATH H.A.H. Salem, On the fractional calculus in abstract spaces and their applications to the Dirichlet-type problem of fractional order. Comput. Math. Appl. 59(3), 1278–1293 (2010)MathSciNetCrossRefMATH
224.
Zurück zum Zitat H.A.H. Salem Global monotonic solutions of multi term fractional differential equations. Appl. Math. Comput. 217(14), 6597–6603 (2011)MathSciNetCrossRef H.A.H. Salem Global monotonic solutions of multi term fractional differential equations. Appl. Math. Comput. 217(14), 6597–6603 (2011)MathSciNetCrossRef
225.
Zurück zum Zitat S.G. Samko, A.A. Kilbas, O.I. Marichev, in Fractional Integrals and Derivatives. Theory and Applications (Gordon and Breach, Yverdon, 1993) S.G. Samko, A.A. Kilbas, O.I. Marichev, in Fractional Integrals and Derivatives. Theory and Applications (Gordon and Breach, Yverdon, 1993)
226.
Zurück zum Zitat N. Samko, S. Samko, B. Vakulov, Fractional integrals and hypersingular integrals in variable order Hlder spaces on homogeneous spaces. J. Funct. Spaces Appl. 8(3), 215–244 (2010)MathSciNetCrossRefMATH N. Samko, S. Samko, B. Vakulov, Fractional integrals and hypersingular integrals in variable order Hlder spaces on homogeneous spaces. J. Funct. Spaces Appl. 8(3), 215–244 (2010)MathSciNetCrossRefMATH
227.
Zurück zum Zitat A.M. Samoilenko, N.A. Perestyuk, in Impulsive Differential Equations (World Scientific, Singapore, 1995) A.M. Samoilenko, N.A. Perestyuk, in Impulsive Differential Equations (World Scientific, Singapore, 1995)
228.
Zurück zum Zitat N.P. Semenchuk, On one class of differential equations of noninteger order. Differents. Uravn. 10, 1831–1833 (1982)MathSciNet N.P. Semenchuk, On one class of differential equations of noninteger order. Differents. Uravn. 10, 1831–1833 (1982)MathSciNet
229.
Zurück zum Zitat H. Sheng, Y. Chen, T. Qiu, in Fractional Processes and Fractional-order Signal Processing; Techniques and Applications (Springer-Verlag, London, 2011) H. Sheng, Y. Chen, T. Qiu, in Fractional Processes and Fractional-order Signal Processing; Techniques and Applications (Springer-Verlag, London, 2011)
230.
Zurück zum Zitat B.A. Slimani, A contribution to fractional order differential equations and inclusions with impulses, Doctorate thesis, University of Sidi Bel Abbes, 2009 B.A. Slimani, A contribution to fractional order differential equations and inclusions with impulses, Doctorate thesis, University of Sidi Bel Abbes, 2009
231.
Zurück zum Zitat V.E. Tarasov, in Fractional dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media (Springer, Heidelberg, 2010) V.E. Tarasov, in Fractional dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media (Springer, Heidelberg, 2010)
233.
Zurück zum Zitat V.E. Tarasov, M. Edelman, Fractional dissipative standard map. Chaos 20(2), 023127, 7 (2010) V.E. Tarasov, M. Edelman, Fractional dissipative standard map. Chaos 20(2), 023127, 7 (2010)
234.
Zurück zum Zitat J.A. Tenreiro Machado, Time-delay and fractional derivatives. Adv. Difference Equ. 2011, Art. ID 934094, 12 pp J.A. Tenreiro Machado, Time-delay and fractional derivatives. Adv. Difference Equ. 2011, Art. ID 934094, 12 pp
235.
Zurück zum Zitat J.A. Tenreiro Machado. Entropy analysis of integer and fractional dynamical systems. Nonlinear Dynam. 62(1–2), 371–378 (2010)MathSciNetCrossRefMATH J.A. Tenreiro Machado. Entropy analysis of integer and fractional dynamical systems. Nonlinear Dynam. 62(1–2), 371–378 (2010)MathSciNetCrossRefMATH
236.
Zurück zum Zitat J.A. Tenreiro Machado. Time-delay and fractional derivatives. Adv. Difference Equ. (2011), Art. ID 934094, 12 pp J.A. Tenreiro Machado. Time-delay and fractional derivatives. Adv. Difference Equ. (2011), Art. ID 934094, 12 pp
237.
Zurück zum Zitat J.A. Tenreiro Machado, V. Kiryakova, F. Mainardi, A poster about the old history of fractional calculus. Fract. Calc. Appl. Anal. 13(4), 447–454 (2010)MathSciNetMATH J.A. Tenreiro Machado, V. Kiryakova, F. Mainardi, A poster about the old history of fractional calculus. Fract. Calc. Appl. Anal. 13(4), 447–454 (2010)MathSciNetMATH
238.
Zurück zum Zitat J.A. Tenreiro Machado, V. Kiryakova, F. Mainardi, Recent history of fractional calculus. Commun. Nonlinear Sci. Numer. Simul. 16(3), 1140–1153 (2011)MathSciNetCrossRefMATH J.A. Tenreiro Machado, V. Kiryakova, F. Mainardi, Recent history of fractional calculus. Commun. Nonlinear Sci. Numer. Simul. 16(3), 1140–1153 (2011)MathSciNetCrossRefMATH
239.
Zurück zum Zitat J.A. Tenreiro Machado, V. Kiryakova, F. Mainardi, A poster about the old history of fractional calculus. Fract. Calc. Appl. Anal. 13(4), 447–454 (2010)MathSciNetMATH J.A. Tenreiro Machado, V. Kiryakova, F. Mainardi, A poster about the old history of fractional calculus. Fract. Calc. Appl. Anal. 13(4), 447–454 (2010)MathSciNetMATH
240.
Zurück zum Zitat J.C. Trigeassou, N. Maamri, J. Sabatier, A.A. Oustaloup, Lyapunov approach to the stability of fractional differential equations. Signal Process. 91, 437–445 (2011)CrossRefMATH J.C. Trigeassou, N. Maamri, J. Sabatier, A.A. Oustaloup, Lyapunov approach to the stability of fractional differential equations. Signal Process. 91, 437–445 (2011)CrossRefMATH
241.
Zurück zum Zitat L. Vzquez. From Newton’s equation to fractional diffusion and wave equations. Adv. Difference Equ. 2011, Art. ID 169421, 13 pp L. Vzquez. From Newton’s equation to fractional diffusion and wave equations. Adv. Difference Equ. 2011, Art. ID 169421, 13 pp
242.
Zurück zum Zitat A.N. Vityuk, On solutions of hyperbolic differential inclusions with a nonconvex right-hand side (Russian) Ukran. Mat. Zh. 47(4), 531–534 (1995); translation in Ukrainian Math. J. 47 (1995), no. 4, 617–621 (1996) A.N. Vityuk, On solutions of hyperbolic differential inclusions with a nonconvex right-hand side (Russian) Ukran. Mat. Zh. 47(4), 531–534 (1995); translation in Ukrainian Math. J. 47 (1995), no. 4, 617–621 (1996)
243.
Zurück zum Zitat A.N. Vityuk, Existence of Solutions of partial differential inclusions of fractional order. Izv. Vyssh. Uchebn. Ser. Mat. 8, 13–19 (1997)MathSciNet A.N. Vityuk, Existence of Solutions of partial differential inclusions of fractional order. Izv. Vyssh. Uchebn. Ser. Mat. 8, 13–19 (1997)MathSciNet
244.
Zurück zum Zitat A.N. Vityuk, A.V. Golushkov, Existence of solutions of systems of partial differential equations of fractional order. Nonlinear Oscil. 7(3), 318–325 (2004)MathSciNetCrossRef A.N. Vityuk, A.V. Golushkov, Existence of solutions of systems of partial differential equations of fractional order. Nonlinear Oscil. 7(3), 318–325 (2004)MathSciNetCrossRef
245.
Zurück zum Zitat A.N. Vityuk, A.V. Golushkov, The Darboux problem for a differential equation containing a fractional derivative. Nonlinear Oscil. 8, 450–462 (2005)MathSciNetCrossRef A.N. Vityuk, A.V. Golushkov, The Darboux problem for a differential equation containing a fractional derivative. Nonlinear Oscil. 8, 450–462 (2005)MathSciNetCrossRef
246.
Zurück zum Zitat A.N. Vityuk, A.V. Mykhailenko, On one class of differential quations of fractional order. Nonlinear Oscil. 11(3) (2008), 307–319MathSciNetCrossRef A.N. Vityuk, A.V. Mykhailenko, On one class of differential quations of fractional order. Nonlinear Oscil. 11(3) (2008), 307–319MathSciNetCrossRef
247.
Zurück zum Zitat A.N. Vityuk, A.V. Mykhailenko, The Darboux problem for an implicit fractional-order differential equation. J. Math. Sci. 175(4), 391–401 (2011)CrossRef A.N. Vityuk, A.V. Mykhailenko, The Darboux problem for an implicit fractional-order differential equation. J. Math. Sci. 175(4), 391–401 (2011)CrossRef
248.
Zurück zum Zitat J. Wang, Y. Zhou, W. Wei, A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces. Commun. Nonlinear Sci. Numer. Simul. 16(10), 4049–4059 (2011)MathSciNetCrossRefMATH J. Wang, Y. Zhou, W. Wei, A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces. Commun. Nonlinear Sci. Numer. Simul. 16(10), 4049–4059 (2011)MathSciNetCrossRefMATH
250.
Zurück zum Zitat G. Zaslavsky, in Hamiltonian Chaos and Fractional Dynamics (Oxford University Press, New York, 2005)MATH G. Zaslavsky, in Hamiltonian Chaos and Fractional Dynamics (Oxford University Press, New York, 2005)MATH
251.
Zurück zum Zitat S. Zhang, Positive solutions for boundary-value problems of nonlinear fractional diffrential equations. Electron. J. Differ. Equat. (36), 1–12 (2006) S. Zhang, Positive solutions for boundary-value problems of nonlinear fractional diffrential equations. Electron. J. Differ. Equat. (36), 1–12 (2006)
252.
Zurück zum Zitat S. Zhang, Existence of positive solutions of a singular partial differential equation. Math. Bohemica 133(1), 29–40 (2008)MATH S. Zhang, Existence of positive solutions of a singular partial differential equation. Math. Bohemica 133(1), 29–40 (2008)MATH
253.
Zurück zum Zitat Y. Zhou, Existence and uniqueness of fractional functional differential equations with unbounded delay. Int. J. Dyn. Syst. Differ. Equat. 1(4), 239–244 (2008)MATH Y. Zhou, Existence and uniqueness of fractional functional differential equations with unbounded delay. Int. J. Dyn. Syst. Differ. Equat. 1(4), 239–244 (2008)MATH
254.
Zurück zum Zitat Y. Zhou, F. Jiao, J. Li, Existence and uniqueness for p-type fractional neutral differential equations. Nonlinear Anal. 71, 2724–2733 (2009)MathSciNetCrossRefMATH Y. Zhou, F. Jiao, J. Li, Existence and uniqueness for p-type fractional neutral differential equations. Nonlinear Anal. 71, 2724–2733 (2009)MathSciNetCrossRefMATH
255.
Zurück zum Zitat Y. Zhou, F. Jiao, J. Li, Existence and uniqueness for fractional neutral differential equations with infinite delay. Nonlinear Anal. 71, 3249–3256 (2009)MathSciNetCrossRefMATH Y. Zhou, F. Jiao, J. Li, Existence and uniqueness for fractional neutral differential equations with infinite delay. Nonlinear Anal. 71, 3249–3256 (2009)MathSciNetCrossRefMATH
Metadaten
Titel
Impulsive Partial Hyperbolic Functional Differential Equations
verfasst von
Saïd Abbas
Mouffak Benchohra
Gaston M. N’Guérékata
Copyright-Jahr
2012
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-4036-9_5