Analyzing Coupled Delayed Fractional Systems: Theoretical Insights and Numerical Approaches

Meraa Arab, Mohammed S. Abdo (), Najla Alghamdi and Muath Awadalla ()
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Meraa Arab: Department of Mathematics and Statistics, College of Science, King Faisal University, Ahsa 31982, Saudi Arabia
Mohammed S. Abdo: Department of Mathematics, Hodeidah University, Al Hudaydah 3114, Yemen
Najla Alghamdi: Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia
Muath Awadalla: Department of Mathematics and Statistics, College of Science, King Faisal University, Ahsa 31982, Saudi Arabia

Mathematics, 2025, vol. 13, issue 7, 1-17

Abstract: In this work, we investigate the theoretical properties of a generalized coupled system of finite-delay fractional differential equations involving Caputo derivatives. We establish rigorous criteria to ensure the existence and uniqueness of solutions under appropriate assumptions on the problem parameters and constituent functions, employing contraction mapping principles and Schauder’s fixed-point theorem. Then, we examine the Ulam–Hyers stability of the proposed system. To illustrate the main findings, three examples are provided. Moreover, we provide numerical solutions using the Adams–Bashforth–Moulton method. The practical significance of our results is demonstrated through illustrative examples, highlighting applications in predator–prey dynamics and control systems.

Keywords: Caputo fractional derivative; existence and stability; fixed-point theorems; Adams–Bashforth–Moulton method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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