Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces

Abstract

In this paper, we establish the existence of piece wise (PC)-mild solutions (defined in Section 2) for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained using techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we used the distributed characteristic operators to define a mild solution of the system. We also discussed the controversy related to the solution operator for the fractional order system using weak and strong Caputo derivatives. Examples are given to illustrate the theory.