Existence results for fractional order semilinear integro-differential evolution equations with infinite delay

摘要

This paper is concerned with existence results of mild solutions for fractional order semilinear integro-differential evolution equations (FSIDEEs) and semilinear neutral integro-differential evolution equations (FSNIDEEs in short) with infinite delay in α-norm. Our tools include the Banach contraction principle, the nonlinear alternative of Leray-Schauder type and the Krasnoselskii-Schaefer type fixed point theorem.