Existence and Stability Analysis of Nonlinear Systems with Hadamard Fractional Derivatives

Mouataz Billah Mesmouli, Ioan-Lucian Popa () and Taher S. Hassan
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Mouataz Billah Mesmouli: Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia
Ioan-Lucian Popa: Department of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, Romania
Taher S. Hassan: Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia

Mathematics, 2025, vol. 13, issue 11, 1-12

Abstract: This paper investigates the existence, uniqueness, and finite-time stability of solutions to a class of nonlinear systems governed by the Hadamard fractional derivative. The analysis is carried out using two fundamental tools from fixed point theory: the Krasnoselskii fixed point theorem and the Banach contraction principle. These methods provide rigorous conditions under which solutions exist and are unique. Furthermore, criteria ensuring the finite-time stability of the system are derived. To demonstrate the practicality of the theoretical results, a detailed example is presented. This paper also discusses certain assumptions and presents corollaries that naturally emerge from the main theorems.

Keywords: Hadamard fractional derivative; nonlinear system; existence and uniqueness; finite-time stability; fixed point theorems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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