10.57647/mathsci.2026.2004.22
On the Existence and Stability of Solutions for Implicit Coupled Neutral Fractional Differential Systems
- Hasanen A. Hammad
1,2 - Sami Baraket3
- Hassen Aydi*4
- Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
- Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
- Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11623, Saudi Arabia
- Universit´e de Sousse, Institut Sup´erieur d’Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
Received: 2026-02-22
Revised: 2026-04-26
Accepted: 2026-05-14
Published Online: 2026-05-25
Copyright (c) 2026 Hasanen A. Hammad, Sami Baraket, Hassen Aydi (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
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Abstract
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
Keywords
- Fractional derivative,
- Fixed point,
- Stability analysis,
- Neutral fractional differential equation