Some results for impulsive fractional differential inclusions with infinite delay and sectorial operators in Banach spaces

Abstract

This paper is concerned with impulsive fractional differential inclusions with sectorial operators, nonlocal conditions and infinite delay in Banach spaces. Using tools involving the measure of noncompactness and multi-valued fixed point theory, we derive some existence results of PC-mild solutions when the multivalued map F is convex as well as nonconvex. Furthermore, the compactness of the set of solutions and continuous dependence results are also obtained. As an application, an impulsive neutral partial functional differential equation is also investigated at last.