Existence and stability of solutions of ψ-Hilfer fractional functional differential inclusions with non-instantaneous impulses

Abstract

In this paper, we prove two existence results of solutions for an ψ-Hilfer fractional non-instantaneous impulsive differential inclusion in the presence of delay in an infinite dimensional Banah spaces. Then, by using the multivalued weakly Picard operator theory, we study the stability of solutions for the considered problem in the sense of ψ-generalized Ulam-Hyers. To achieve our aim, we present a relation between any solution of the considered problem and the corresponding fractional integral equation. The given problem here is new because it contains a delay and non-instantaneous impulses effect. Examples are given to clarify the possibility of applicability our assumptions.

Keywords

• non-instantaneous impulsive differential inclusion
• ψ−hilfer fractional derivative
• ulam-hyers-rassias stability
• muktivalued weakly picard operators