Existence of solutions for nonlocal semilinear fractional integro-differential equation with Krasnoselskii-Krein-type conditions

Abstract

In this paper, we are mainly focused upon the existence and uniqueness of mild solutions to a semilinear fractional integro-differential equations with nonlocal conditions in Banach spaces. Based upon suitable fixed point thereoms combined with the study of an α-resolvent family, the main results are established under the Krasnoselskii-Krein-type conditions.