Existence of mild solutions for semilinear ψ−Caputo-type fractional evolution equations with nonlocal conditions in Banach spaces

Abstract

The main crux of this manuscript is to investigate the existence of mild solutions for a class of semilinear ψ−Caputo-type fractional evolution equations in Banach spaces with nonlocal conditions. The proofs are based on Krasnoselskii xed point theorem, compact semigroup, generalized ψ−Laplace transform and certain fundamental ψ−fractional calculus tools. As application, a nontrivial example is given to illustrate our theoretical results.