OICC Press Mathematical Sciences 2251-7456 2026 07 15 On the Existence and Stability of Solutions for Implicit Coupled Neutral Fractional Differential Systems 10.57647/mathsci.2026.2004.22 EN Hasanen A. Hammad Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia; Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt https://orcid.org/0000-0001-8724-9367 Sami Baraket Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11623, Saudi Arabia Hassen Aydi Universit´e de Sousse, Institut Sup´erieur d’Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia Journal Article 2026 07 15 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