Résumé:
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
