Existence results for Atangana-Baleanu fractional neutral integro-differential systems with infinite delay through sectorial operators

Abstract

This manuscript’s main objective is to examine the existence of mild solution of Atangana-Baleanu fractional order semi-linear integro-differential equations [ABFSIDE] and semi-linear neutral integro-differential evolution equations [ABFSNIDE] with infinite delay [ID] in Banach spaces. We introduce an appropriate definition of a mild solution for these systems. Based on the Banach contraction principle, nonlinear alternative of Leray-Schauder type and Krasnoselskii-Schaefer fixed point theorem joined with ρ-resolvent operators, we develop the main results. Finally, an example is given to justify the theoretical results.