Existence of solutions to differential inclusions with fractional order and impulses

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.

Keywords

• Initial value problem
• impulses
• differential inclusion
• Caputo fractional derivative
• fractional integral
• existence
• uniqueness
• fixed point