Analysis of an Abstract Delayed Fractional Integro-Differential System via the α-Resolvent Operator

This paper explores the mild solutions of partial impulsive fractional integro-differential systems of order 1<α<2 in a Banach space. We derive the solution of the system under the assumption that the homogeneous part of the system admits an α-resolvent operator. Krasnoselskii’s fixed point theorem is used for the existence of solution, while uniqueness is ensured using Banach’s fixed point theorem. The stability of the system is analyzed through the framework of Hyers–Ulam stability using Lipschitz conditions. Finally, examples are presented to illustrate the applicability of the theoretical results.