Electron. J. Diff. Equ., Vol. 2010(2010), No. 80, pp. 1-18.

Existence of solutions to differential inclusions with fractional order and impulses

Mouffak Benchohra, Samira Hamani, Juan Jose Nieto, Boualem Attou Slimani

Abstract:
We establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential inclusions involving the Caputo fractional derivative. We consider the cases when the multivalued nonlinear term takes convex values as well as nonconvex values. The topological structure of the set of solutions is also considered.

Submitted March 11, 2010. Published June 15, 2010.
Math Subject Classifications: 26A33, 34A37.
Key Words: Initial value problem; impulses; differential inclusion; Caputo fractional derivative; fractional integral; existence; uniqueness; fixed point.

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Mouffak Benchohra
Laboratoire de Mathématiques, Université de Sidi Bel-Abbès
B.P. 89, 22000, Sidi Bel-Abbès, Algérie
email: benchohra@univ-sba.dz
Samira Hamani
Laboratoire de Mathématiques, Université de Sidi Bel-Abbès
B.P. 89, 22000, Sidi Bel-Abbès, Algérie
email: hamani_samira@yahoo.fr
Juan Jose Nieto
Departamento de Analisis Matematico, Facultad de Matematicas
Universidad de Santiago de Compostela, Santiago de Compostela, Spain
email: juanjose.nieto.roig@usc.es
Boualem Attou Slimani
Facultée des Sciences de l'Ingéenieur, Universitée de Tlemcen
B.P. 119, 13000, Tlemcen, Algéerie
email: ba_slimani@yahoo.fr

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