Abstract
•This research work investigates the existence results for Atangana-Baleanu fractional order semilinear integro-differential equations (ABFSIDE) and semilinear neutral integro-differential evolution equations (ABFSNIDE) with infinite delay (ID) in Banach space.•The key outcomes are established with the aid of Banach contraction, the nonlinear alternative of the Leray-Schauder and Krasnoselskii-Schaefer fixed point theorem coupled with rho-resolvent operators.•To the authors knowledge, no paper exists in Atangana-Baleanu fractional neutral integrodifferential system with infinite delay in literature, and this is the key inspiration of this work. In this manuscript, we present and prove the new mild solution for the system (1.3)-(1.4) in Lemma 4.1 with full details.
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.