Skip to main content
Erschienen in: Journal of Applied Mathematics and Computing 1-2/2014

01.10.2014 | Original Research

On the impulsive fractional anti-periodic BVP modelling with constant coefficients

verfasst von: JinRong Wang, Zeng Lin

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2014

Einloggen

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

search-config
loading …

Abstract

This paper is inspired by the recent papers on the BVP for impulsive fractional differential equations. We present a general framework to find the solutions of anti-periodic BVP for linear impulsive fractional differential equations with constant coefficients. Some sufficient conditions for existence of the solutions for nonlinear problem are established. Finally, numerical examples are given to illustrate the results.

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 "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!

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!

Literatur
1.
Zurück zum Zitat Ahmad, B., Sivasundaram, S.: Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations. Nonlinear Anal. 3, 251–258 (2009) MATHMathSciNet Ahmad, B., Sivasundaram, S.: Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations. Nonlinear Anal. 3, 251–258 (2009) MATHMathSciNet
2.
Zurück zum Zitat Ahmad, B., Sivasundaram, S.: Existence of solutions for impulsive integral boundary value problems of fractional order. Nonlinear Anal. 4, 134–141 (2010) MATHMathSciNet Ahmad, B., Sivasundaram, S.: Existence of solutions for impulsive integral boundary value problems of fractional order. Nonlinear Anal. 4, 134–141 (2010) MATHMathSciNet
3.
Zurück zum Zitat Ahmad, B., Wang, G.: Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order. Comput. Math. Appl. 59, 1341–1349 (2010) MathSciNet Ahmad, B., Wang, G.: Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order. Comput. Math. Appl. 59, 1341–1349 (2010) MathSciNet
4.
Zurück zum Zitat Tian, Y., Bai, Z.: Existence results for the three-point impulsive boundary value problem involving fractional differential equations. Comput. Math. Appl. 59, 2601–2609 (2010) CrossRefMATHMathSciNet Tian, Y., Bai, Z.: Existence results for the three-point impulsive boundary value problem involving fractional differential equations. Comput. Math. Appl. 59, 2601–2609 (2010) CrossRefMATHMathSciNet
5.
Zurück zum Zitat Cao, J., Chen, H.: Some results on impulsive boundary value problem for fractional differential inclusions. Electron. J. Qual. Theory Differ. Equ. 2010(11), 1–24 (2010) Cao, J., Chen, H.: Some results on impulsive boundary value problem for fractional differential inclusions. Electron. J. Qual. Theory Differ. Equ. 2010(11), 1–24 (2010)
6.
Zurück zum Zitat Wang, G., Ahmad, B., Zhang, L.: Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order. Nonlinear Anal. 74, 792–804 (2011) CrossRefMATHMathSciNet Wang, G., Ahmad, B., Zhang, L.: Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order. Nonlinear Anal. 74, 792–804 (2011) CrossRefMATHMathSciNet
7.
Zurück zum Zitat Wang, G., Zhang, L., Song, G.: Systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions. Nonlinear Anal. 74, 974–982 (2011) CrossRefMATHMathSciNet Wang, G., Zhang, L., Song, G.: Systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions. Nonlinear Anal. 74, 974–982 (2011) CrossRefMATHMathSciNet
8.
Zurück zum Zitat Wang, G., Ahmad, B., Zhang, L.: Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions. Comput. Math. Appl. 59, 1389–1397 (2010) CrossRefMathSciNet Wang, G., Ahmad, B., Zhang, L.: Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions. Comput. Math. Appl. 59, 1389–1397 (2010) CrossRefMathSciNet
9.
Zurück zum Zitat Wang, X.: Impulsive boundary value problem for nonlinear differential equations of fractional order. Comput. Math. Appl. 62, 2383–2391 (2011) CrossRefMATHMathSciNet Wang, X.: Impulsive boundary value problem for nonlinear differential equations of fractional order. Comput. Math. Appl. 62, 2383–2391 (2011) CrossRefMATHMathSciNet
10.
Zurück zum Zitat Cao, J., Chen, H.: Impulsive fractional differential equations with nonlinear boundary conditions. Math. Comput. Model. 55, 303–311 (2012) CrossRefMATHMathSciNet Cao, J., Chen, H.: Impulsive fractional differential equations with nonlinear boundary conditions. Math. Comput. Model. 55, 303–311 (2012) CrossRefMATHMathSciNet
11.
Zurück zum Zitat Yang, L., Chen, H.: Nonlocal boundary value problem for impulsive differential equations of fractional order. Adv. Differ. Equ. 2011, 404917 (2011) Yang, L., Chen, H.: Nonlocal boundary value problem for impulsive differential equations of fractional order. Adv. Differ. Equ. 2011, 404917 (2011)
12.
Zurück zum Zitat Wang, J., Zhou, Y., Fečkan, M.: On recent developments in the theory of boundary value problems for impulsive fractional differential equations. Comput. Math. Appl. 64, 3008–3020 (2012) CrossRefMATHMathSciNet Wang, J., Zhou, Y., Fečkan, M.: On recent developments in the theory of boundary value problems for impulsive fractional differential equations. Comput. Math. Appl. 64, 3008–3020 (2012) CrossRefMATHMathSciNet
13.
Zurück zum Zitat Fečkan, M., Zhou, Y., Wang, J.: On the concept and existence of solution for impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 17, 3050–3060 (2011) Fečkan, M., Zhou, Y., Wang, J.: On the concept and existence of solution for impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 17, 3050–3060 (2011)
14.
Zurück zum Zitat Kosmatov, N.: Initial value problems of fractional order with fractional impulsive conditions. Results Math. 63, 1289–1310 (2013) CrossRefMATHMathSciNet Kosmatov, N.: Initial value problems of fractional order with fractional impulsive conditions. Results Math. 63, 1289–1310 (2013) CrossRefMATHMathSciNet
15.
Zurück zum Zitat Wang, J., Fečkan, M., Zhou, Y.: On the new concept of solutions and existence results for impulsive fractional evolution equations. Dyn. Partial Differ. Equ. 8, 345–361 (2011) CrossRefMATHMathSciNet Wang, J., Fečkan, M., Zhou, Y.: On the new concept of solutions and existence results for impulsive fractional evolution equations. Dyn. Partial Differ. Equ. 8, 345–361 (2011) CrossRefMATHMathSciNet
16.
Zurück zum Zitat Wang, J., Zhou, Y., Fečkan, M.: Nonlinear impulsive problems for fractional differential equations and Ulam stability. Comput. Math. Appl. 64, 3389–3405 (2012) CrossRefMATHMathSciNet Wang, J., Zhou, Y., Fečkan, M.: Nonlinear impulsive problems for fractional differential equations and Ulam stability. Comput. Math. Appl. 64, 3389–3405 (2012) CrossRefMATHMathSciNet
17.
Zurück zum Zitat Wang, J., Li, X.Z., Wei, W.: On the natural solution of an impulsive fractional differential equation of order q∈(1,2). Commun. Nonlinear Sci. Numer. Simul. 17, 4384–4394 (2012) CrossRefMATHMathSciNet Wang, J., Li, X.Z., Wei, W.: On the natural solution of an impulsive fractional differential equation of order q∈(1,2). Commun. Nonlinear Sci. Numer. Simul. 17, 4384–4394 (2012) CrossRefMATHMathSciNet
18.
Zurück zum Zitat Li, X.P., Chen, F.L., Li, X.Z.: Generalized anti-periodic boundary value problems of impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 18, 28–41 (2013) CrossRefMATHMathSciNet Li, X.P., Chen, F.L., Li, X.Z.: Generalized anti-periodic boundary value problems of impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 18, 28–41 (2013) CrossRefMATHMathSciNet
19.
Zurück zum Zitat Stamova, I., Stamov, G.: Stability analysis of impulsive functional systems of fractional order. Commun. Nonlinear Sci. Numer. Simul. 19, 702–709 (2014) CrossRefMathSciNet Stamova, I., Stamov, G.: Stability analysis of impulsive functional systems of fractional order. Commun. Nonlinear Sci. Numer. Simul. 19, 702–709 (2014) CrossRefMathSciNet
20.
21.
Zurück zum Zitat Baleanu, D., Machado, J.A.T., Luo, A.C.J.: Fractional Dynamics and Control. Springer, Berlin (2012) CrossRefMATH Baleanu, D., Machado, J.A.T., Luo, A.C.J.: Fractional Dynamics and Control. Springer, Berlin (2012) CrossRefMATH
22.
Zurück zum Zitat Diethelm, K.: The analysis of fractional differential equations. Lecture Notes in Mathematics (2010) Diethelm, K.: The analysis of fractional differential equations. Lecture Notes in Mathematics (2010)
23.
Zurück zum Zitat Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier Science, Amsterdam (2006) MATH Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier Science, Amsterdam (2006) MATH
24.
Zurück zum Zitat Lakshmikantham, V., Leela, S., Devi, J.V.: Theory of Fractional Dynamic Systems. Cambridge Scientific, Cambridge (2009) MATH Lakshmikantham, V., Leela, S., Devi, J.V.: Theory of Fractional Dynamic Systems. Cambridge Scientific, Cambridge (2009) MATH
25.
Zurück zum Zitat Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Differential Equations. Wiley, New York (1993) MATH Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Differential Equations. Wiley, New York (1993) MATH
26.
Zurück zum Zitat Michalski, M.W.: Derivatives of noninteger order and their applications. Dissertationes Mathematicae, CCCXXVIII, Inst. Math., Polish Acad. Sci. (1993) Michalski, M.W.: Derivatives of noninteger order and their applications. Dissertationes Mathematicae, CCCXXVIII, Inst. Math., Polish Acad. Sci. (1993)
27.
Zurück zum Zitat Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999) MATH Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999) MATH
28.
Zurück zum Zitat Tarasov, V.E.: Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles. Fields and Media. Springer, Berlin (2011). HEP Tarasov, V.E.: Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles. Fields and Media. Springer, Berlin (2011). HEP
29.
Zurück zum Zitat Zhou, Y., Jiao, F.: Nonlocal Cauchy problem for fractional evolution equations. Nonlinear Anal., Real World Appl. 11, 4465–4475 (2010) CrossRefMATHMathSciNet Zhou, Y., Jiao, F.: Nonlocal Cauchy problem for fractional evolution equations. Nonlinear Anal., Real World Appl. 11, 4465–4475 (2010) CrossRefMATHMathSciNet
30.
Zurück zum Zitat Wang, J., Fec̆kan, M., Zhou, Y.: Presentation of solutions of impulsive fractional Langevin equations and existence results. Eur. Phys. J. Spec. Top. 222, 1855–1872 (2013) Wang, J., Fec̆kan, M., Zhou, Y.: Presentation of solutions of impulsive fractional Langevin equations and existence results. Eur. Phys. J. Spec. Top. 222, 1855–1872 (2013)
31.
Zurück zum Zitat Atkinson, C., Osseiran, A.: Rational solutions for the time-fractional diffusion equation. SIAM J. Appl. Math. 71, 92–106 (2011) CrossRefMATHMathSciNet Atkinson, C., Osseiran, A.: Rational solutions for the time-fractional diffusion equation. SIAM J. Appl. Math. 71, 92–106 (2011) CrossRefMATHMathSciNet
32.
Zurück zum Zitat Lakshmikantham, V., Leela, S.: Differential and Integral Inequalities, vol. 1. Academic Press, New York (1969) MATH Lakshmikantham, V., Leela, S.: Differential and Integral Inequalities, vol. 1. Academic Press, New York (1969) MATH
33.
Zurück zum Zitat Wei, W., Xiang, X., Peng, Y.: Nonlinear impulsive integro-differential equation of mixed type and optimal controls. Optimization 55, 141–156 (2006) CrossRefMATHMathSciNet Wei, W., Xiang, X., Peng, Y.: Nonlinear impulsive integro-differential equation of mixed type and optimal controls. Optimization 55, 141–156 (2006) CrossRefMATHMathSciNet
Metadaten
Titel
On the impulsive fractional anti-periodic BVP modelling with constant coefficients
verfasst von
JinRong Wang
Zeng Lin
Publikationsdatum
01.10.2014
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2014
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-013-0740-7

Weitere Artikel der Ausgabe 1-2/2014

Journal of Applied Mathematics and Computing 1-2/2014 Zur Ausgabe