Impulsive fractional differential inclusions involving the Caputo fractional derivative

Abstract

IMPULSIVE FRACTIONAL DIFFERENTIAL INCLUSIONS INVOLVING THE CAPUTO FRACTIONAL DERIVATIVE 1 E. Ait Dads ∗ , M. Benchohra ∗∗ , S. Hamani ∗∗ Abstract In this paper, we establish sufficient conditions for the existence of solu- tions for a class of initial value problem for impulsive fractional differential inclusions involving the Caputo fractional derivative. Both cases of con- vex and nonconvex valued right-hand side are considered. The topological structure of the set of solutions is also considered. Mathematics Subject Classification : 26A33, 34A37 Key Words and Phrases : initial value problem, fractional differential inclusions, impulses, Caputo fractional derivative, fractional integral, selec- tion, existence, fixed point theorem