Applied Mathematical Techniques for the Stability and Solution of Hybrid Fractional Differential Systems

Mohammad Alakel Abazid (), Muath Awadalla, Murugesan Manigandan () and Jihan Alahmadi
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Mohammad Alakel Abazid: Department of Mathematics and Statistics, College of Science, King Faisal University, Hofuf 31982, Saudi Arabia
Muath Awadalla: Department of Mathematics and Statistics, College of Science, King Faisal University, Hofuf 31982, Saudi Arabia
Murugesan Manigandan: Center for Nonlinear and Complex Networks, SRM TRP Engineering College, Tiruchirapalli 621 105, India
Jihan Alahmadi: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Mathematics, 2025, vol. 13, issue 6, 1-22

Abstract: This paper addresses a coupled system of hybrid fractional differential equations governed by non-local Hadamard-type boundary conditions. The study focuses on proving the existence, uniqueness, and stability of the system’s solutions. To achieve this, we apply Banach’s fixed point theorem and the Leray–Schauder alternative, while the stability is verified through the Ulam–Hyers framework. Additionally, a numerical example is presented to illustrate the practical relevance of the theoretical findings.

Keywords: Hadamard operator; fractional derivative; hybrid; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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