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
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Samira Hamani
Laboratoire de Mathématiques
Université de Sidi Bel-Abbès
B.P. 89, 22000, Sidi Bel-Abbès, Algérie
email: hamani_samira@yahoo.fr
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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
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Boualem Attou Slimani
Faculté des Sciences de l'Ingénieur
Université de Tlemcen
B.P. 119, 13000, Tlemcen, Algérie
email: ba_slimani@yahoo.fr
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