On the Existence and Stability of Solutions for Implicit Coupled Neutral Fractional Differential Systems

This paper investigated the existence, uniqueness, and stability behavior of a class of non-linear implicit coupled neutral fractional differential equations governed by the Caputo-Atangana-Baleanu derivative. The existence of solutions was obtained by applying Krasnoselskii’s fixed-point theorem, whereas the Banach contraction principle was employed to establish both existence and uniqueness results. Furthermore, several important stability concepts were analyzed, namely Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability, and generalized Ulam-Hyers-Rassias stability. To illustrate the applicability of the developed theory, suitable examples were presented, validating the solvability and stability results for the proposed system. MSC (2020): 35A23, 47H10, 47H09, 26A33