Existence and stability for partial functional integro-differential equations of fractional order with multiple time delay

Nonlinear Studies

Volumn 20, Issue 2, 2013, Pages 149-162

  Abbas, Saïd ^a   Benchohra, Mouffak ^b  

^a 2320 Rue de Salaberry apt 10 ^*  (Canada)

^b UNIVERSITY OF SIDI BEL ABBES   (Algeria)

Author keywords

Banach space; Caputo fractional order derivative; Chet space; Fixed point; Fr ; Left sided mixed riemann liouville integral; Partial integro differential equation; Solution; Stability

Indexed keywords

EID: 84880600161     PISSN: 13598678     EISSN: 21534373     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. S. Abbas, D. Baleanu and M. Benchohra, Global attractivity for fractional order delay partial integro-differential equations, Adv. Difference Equ. 2012, 19 pages doi:10.1186/1687-1847-2012-62.
2. S. Abbas and M. Benchohra, Darboux problem for perturbed partial differential equations of fractional order with finite delay, Nonlinear Anal. Hybrid Syst. 3 (2009), 597-604.
3. S. Abbas and M. Benchohra, Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order, Nonlinear Anal. Hybrid Syst. 4 (2010), 406-413.
4. S. Abbas and M. Benchohra, Fractional order Riemann-Liouville integral equations with multiple time delay, Appl. Math. E-Notes 12 (2012), 79-87.
5. S. Abbas, M. Benchohra and J. R. Graef, Integro-differential equations of fractional order, Differ. Equ. Dyn. Syst. 20 (2) (2012), 139-148.
6. S. Abbas, M. Benchohra and J. Henderson, On global asymptotic stability of solutions of nonlinear quadratic Volterra integral equations of fractional order, Comm. Appl. Nonlinear Anal. 19 (2012), 79-89.
7. S. Abbas, M. Benchohra and G.M. N'Guérékata, Topics in Fractional Differential Equations, Developments in Mathematics, 27, Springer, New York, 2012.
8. S. Abbas, M. Benchohra and A. N. Vityuk, On fractional order derivatives and Darboux problem for implicit differential equations. Fract. Calc. Appl. Anal. 15 (2) (2012), 168-182.
9. S. Abbas, M. Benchohra and Y. Zhou, Darboux problem for fractional order neutral functional partial hyperbolic differential equations, Int. J. Dyn. Syst. Differ. Equ. 2 (2009), 301-312.
10. C. Avramescu, Some remarks on a fixed point theorem of Krasnoselskii, Electron. J. Qual. Theory Differ. Equ. 5 (2003), 1-15.
11. M. Benchohra, J. R. Graef and S. Hamani, Existence results for boundary value problems of nonlinear fractional differential equations with integral conditions, Appl. Anal. 87 (7) (2008), 851-863.
12. M. Benchohra, J. Henderson, S.K. Ntouyas and A. Ouahab, Existence results for functional differential equations of fractional order, J. Math. Anal. Appl. 338 (2008), 1340-1350.
13. M. Frigon and A. Granas, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22, (2), (1998), 161-168.
14. A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
15. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
16. D. Henry, Geometric Theory of Semilinear Parabolic Partial Differential Equations, Springer-Verlag, Berlin/New York, 1989.
17. R. W. Ibrahim and H. A. Jalab, Existence of the solution of fractiona integral inclusion with time delay, Misk. Math. Notes 11 (2) (2010), 139-150.
18. A.A. Kilbas, Hari M. Srivastava, and Juan J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
19. A. A. Kilbas and S. A. Marzan, Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions, Differential Equations 41 (2005), 84-89.
20. S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993.
21. A. N. Vityuk and A. V. Golushkov, Existence of solutions of systems of partial differential equations of fractional order, Nonlinear Oscil. 7 (3) (2004), 318-325.