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

This manuscript's main objective is to examine the existence of mild solution of Atangana-Baleanu Received 13 December 2020 fractional order semi-linear integro-differential equations [ABFSIDE] and semi-linear neutral integro- Revised 17 April 2021 differential evolution equations [ABFSNIDE] with infinite delay [ID] in Banach spaces. We introduce an Accepted 4 May 2021 appropriate definition of a mild solution for these systems. Based on the Banach contraction principle, Available online 9 June 2021 nonlinear alternative of Leray-Schauder type and Krasnoselskii-Schaefer fixed point theorem joined with 2010 MSC: rho-resolvent operators, we develop the main results. Finally, an example is given to justify the theoretical 34G20 results. (C) 2021 Elsevier Ltd. All rights reserved.