Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 1-2/2017

05.07.2016 | Original Research

p-Moment exponential stability of Caputo fractional differential equations with noninstantaneous random impulses

verfasst von: Ravi Agarwal, Snezhana Hristova, Donal O’Regan

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2017

Einloggen

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

search-config
loading …

Abstract

Stability of Caputo fractional differential equations with impulses occurring at random moments and with non-instantaneous time of their action is studied. Using queuing theory and the usual distribution for waiting time, we study the case of exponentially distributed random variables between two consecutive moments of impulses. The p-moment exponential stability of the zero solution is defined and studied when the waiting time between two consecutive impulses is exponentially distributed and the length of the action of any impulse is initially given. The argument is based on Lyapunov functions. Some examples are given to illustrate our results.
Vorheriger Artikel Global asymptotic stability of the higher order equation
Nächster Artikel Oscillation criteria for third order neutral Emden–Fowler delay dynamic equations on time scales

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!

Jetzt informieren

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!

Jetzt informieren

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!

Jetzt informieren
Literatur
1.
Agarwal, R., Benchohra, M., Slimani, B.A.: Existence results for differential equations with fractional order and impulses. Mem. Differ. Equ. Math. Phys. 44, 1–21 (2008)MathSciNetCrossRefMATH
2.
Agarwal, R., O’Regan, D., Hristova, S.: Stability of Caputo fractional differential equations with non-instantaneous impulses. Commun. Appl. Anal. (accepted)
3.
Agarwal, R., Hristova, S., O’Regan, D.: Lyapunov functions and strict stability of Caputo fractional differential equations. Adv. Differ. Equ. 2015, 20 (2015)
4.
Agarwal, R., O’Regan, D., Hristova, S.: Stability by Lyapunov like functions of nonlinear differential equations with non-instantaneous impulses. J. Appl. Math. Comput. 22 (2015)
5.
Agarwal, R., O’Regan, D., Hristova, S.: Stability of Caputo fractional differential equations by Lyapunov functions. Appl. Math. 60(6), 653–676 (2015)MathSciNetCrossRefMATH
6.
Agarwal, R., Hristova, S., O’Regan, D.: Practical stability of Caputo fractional differential equations by Lyapunov functions. Differ. Equ. Appl. 8(1), 53–68 (2016)MathSciNetMATH
7.
Aguila-Camacho, N., Duarte-Mermoud, M.A., Gallegos, J.A.: Lyapunov functions for fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 19, 2951–2957 (2014)MathSciNetCrossRef
8.
Ahmad, B., Sivasundaram, S.: Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations. Nonlinear Anal. Hybrid Syst. 3, 251–258 (2009)MathSciNetCrossRefMATH
9.
Anguraj, A., Vinodkumar, A.: Existence, uniqueness and stability results of random impulsive semilinear differential systems. Nonlinear Anal. Hybrid Syst. 3, 475–483 (2010)MathSciNetCrossRefMATH
10.
Anguraj, A., Ranjini, M.C., Rivero, M., Trujillo, J.J.: Existence results for fractional neutral functional differential equations with random impulses. Mathematics 2015(3), 16–28 (2015)CrossRefMATH
11.
Bagley, R.L., Calico, R.A.: Fractional order state equations for the control of viscoelastically damped structures. J. Guid. Control Dyn. 14(2), 304–311 (1991)CrossRef
12.
Baleanu, D., Mustafa, O.G.: On the global existence of solutions to a class of fractional differential equations. Comput. Math. Appl. 59, 1835–1841 (2010)MathSciNetCrossRefMATH
13.
Benchohra, M., Slimani, B.A.: Existence and uniqueness of solutions to impulsive fractional differential equations. Electron. J. Differ. Equ. 2009(10), 1–11 (2009)MathSciNetMATH
14.
Church, K.E.M., Smith, R.J.: Existence and uniqueness of solutions of general impulsive extension equations with specification to linear equations. Dyn. Contin. Discrete Impuls. Syst. B 22, 163–197 (2015)MATH
15.
16.
Das, S., Pandey, D.N., Sukavanam, N.: Existence of solution of impulsive second order neutral integro-differential equations with state delay. J. Integral Equ. Appl. 27(4), 489–520 (2015)MathSciNetMATH
17.
De La Sen, M., Luo, N.: A note on the stability of linear time delay systems with impulsive inputs. IEEE Trans. Circuits Syst. I 50(1), 149–152 (2003)MathSciNetCrossRefMATH
18.
Devi, J.V., Mc Rae, F.A., Drici, Z.: Generalized quasilinearization for fractional differential equations. Comput. Math. Appl. 59, 1057–1062 (2010)MathSciNetCrossRefMATH
19.
Devi, J.V., Mc Rae, F.A., Drici, Z.: Variational Lyapunov method for fractional differential equations. Comput. Math. Appl. 64, 2982–2989 (2012)MathSciNetCrossRefMATH
20.
Diethelm, K.: The Analysis of Fractional Differential Equations. Springer, Berlin (2010)CrossRefMATH
21.
Duarte-Mermoud, M.A., Aguila-Camacho, N., Gallegos, J.A., Castro-Linares, R.: Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 22, 650–659 (2015)MathSciNetCrossRefMATH
22.
Feckan, M., Zhou, Y., Wang, J.: On the concept and existence of solution for impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 17(7), 3050–3060 (2012)MathSciNetCrossRefMATH
23.
Feckan, M., Zhou, Y., Wang, J.: Response to “Comments on the concept of existence of solution for impulsive fractional differential equations [Commun Nonlinear Sci Numer Simul 2014;19:4013]”. Commun. Nonlinear Sci. Numer. Simul. 19, 4213–4215 (2014)MathSciNetCrossRef
24.
Hernandez, E., O’Regan, D.: On a new class of abstract impulsive differential equations. Proc. Amer. Math. Soc. 141, 1641–1649 (2013)MathSciNetCrossRefMATH
25.
Hristova, S.: Qualitative Investigations and Approximate Methods for Impulsive Differential Equations. Nova Science Publishers, New York (2009)
26.
Hristova, S.: Integral stability in terms of two measures for impulsive functional differential equations. Math. Comput. Model. 51(1–2), 100–108 (2010)MathSciNetCrossRefMATH
27.
Hristova, S.: Stability on a cone in terms of two measures for impulsive differential equations with ‘supremum’. Appl. Math. Lett. 23(5), 508–511 (2010)MathSciNetCrossRefMATH
28.
Hristova, S.: Razumikhin method and cone valued Lyapunov functions for impulsive differential equations with ‘supremum’. Int. J. Dyn. Syst. Differ. Equ. 2(3–4), 223–236 (2009)MathSciNetMATH
29.
Hristova, S., Stefanova, K.: Practical stability of impulsive differential equations with ‘supremum’ by integral inequalities. Eur. J. Pure Appl. Math. 5(1), 30–44 (2012)MathSciNetMATH
30.
Hristova, S.: Lipschitz stability for impulsive differential equations with ‘supremum’. Int. Electron. J. Pure Appl. Math. 1(4), 345–358 (2010)MATH
31.
Hristova, S., Georgieva, A.: Practical stability in terms of two measures for impulsive differential equations with ‘supremum’. Int. J. Differ. Equ. 2011 (2011)
32.
33.
Kumar, P., Pandey, D.N., Bahuguna, D.: On a new class of abstract impulsive functional differential equations of fractional order. J. Nonlinear Sci. Appl. 7, 10–114 (2014)MathSciNetMATH
34.
Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)CrossRefMATH
35.
Lakshmikantham, V., Leela, S., Devi, J.V.: Theory of Fractional Dynamical Systems. Cambridge Scientific Publishers, Cambridge (2009)MATH
36.
37.
Li, P., Xu, Ch.: Boundary value problems of fractional order differential equation with integral boundary conditions and not instantaneous impulses. J. Funct. Spaces 2015, 9 (2015)
38.
39.
Pierri, M., Henriquez, H.R., Prokopczyk, A.: Global solutions for abstract differential equations with non-instantaneous impulses. Mediterr. J. Math. 1–24 (2015)
40.
Podlubny, I.: Fractional Differential Equations. Academic, San Diego (1999)MATH
41.
Sanz-Serna, J.M., Stuart, A.M.: Ergodicity of dissipative differential equations subject to random impulses. J. Differ. Equ. 155, 262–284 (1999)MathSciNetCrossRefMATH
42.
Wu, S., Hang, D., Meng, X.: p-Moment stability of stochastic equations with jumps. Appl. Math. Comput. 152, 505–519 (2004)MathSciNetMATH
43.
Wu, H., Sun, J.: p-Moment stability of stochastic differential equations with impulsive jump and Markovian switching. Automatica 42, 1753–1759 (2006)MathSciNetCrossRefMATH
44.
Yang, J., Zhong, S., Luo, W.: Mean square stability analysis of impulsive stochastic differential equations with delays. J. Comput. Appl. Math. 216(2), 474–483 (2008)MathSciNetCrossRefMATH
45.
Wang, G., Ahmad, B., Zhang, L., Nieto, J.: Comments on the concept of existence of solution for impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 19, 401–403 (2014)MathSciNetCrossRef
46.
Wang, J.R., Feckan, M., Zhou, Y.: Random noninstantaneous impulsive models for studying periodic evolution processes in pharmacotherapy. Math. Model. Appl. Nonlinear Dyn. Ser. Nonlinear Syst. Complex. 14, 87–107 (2016)MathSciNet
Metadaten
Titel
p-Moment exponential stability of Caputo fractional differential equations with noninstantaneous random impulses
verfasst von
Ravi Agarwal
Snezhana Hristova
Donal O’Regan
Publikationsdatum
05.07.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2017
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-016-1030-y

Weitere Artikel der Ausgabe 1-2/2017

Journal of Applied Mathematics and Computing 1-2/2017 Zur Ausgabe

Original Research

On the number of spanning trees in graphs with multiple edges

Original Research

Impulsive fractional boundary value problem with p-Laplace operator

Original Research

Analysis of time delay in viral infection model with immune impairment

Original Research

Stable manifolds results for planar Hadamard fractional differential equations

Original Research

A new smoothing and regularization Newton method for the symmetric cone complementarity problem

Original Research

Complete weight enumerators of a class of three-weight linear codes