Existence of mild solutions for fractional integrodifferential equations of Sobolev type with nonlocal conditions

Abstract

This paper is concerned with the fractional integrodifferential equations of Sobolev type with nonlocal condition in a separable Banach space. With the help of the theory of propagation family as well as the theory of the measures of noncompactness and the condensing maps, we obtain the existence result of mild solutions for above equations. Two examples are given to illustrate the existence theorem.