Sobolev type fractional integro-differential systems with nonlocal condition through resolvent operators

Abstract

This paper explores the new existence and uniqueness of mild solutions for a class of Sobolev type fractional integro-differential equation (STFIDE) with nonlocal conditions (NLCs) in Banach spaces. By employing the Banach contraction principle and Krasnoselskii fixed point theorem (FPT) coupled with resolvent operators, we build up the desired outcomes. At last, an illustration is also provided to exhibit the attained theorem.