Existence of mild solution for nonlocal impulsive fractional semilinear differential inclusion in Banach space

Abstract

In this paper, we deal with the existence of PC-mild solutions of nonlocal impulsive differential inclusions in Banach space when the values of the orient field is convex (P). By using methods and results of semilinear differential inclusions, and techniques of fixed point theorems, we establish sufficient conditions that guarantee the existence of PC-mild solutions of (P). Our results develop and extend various results proved recently.