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Volume 13
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Article

Existence and Stability Analysis of Nonlinear Systems with Hadamard Fractional Derivatives

by
Mouataz Billah Mesmouli
1,
Ioan-Lucian Popa
2,3,* and
Taher S. Hassan
1,4
1
Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia
2
Department of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, Romania
3
Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania
4
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(11), 1869; https://doi.org/10.3390/math13111869
Submission received: 7 April 2025 / Revised: 23 May 2025 / Accepted: 26 May 2025 / Published: 3 June 2025
Versions Notes

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 Hadamard fractional derivative; nonlinear system; existence and uniqueness; finite-time stability; fixed point theorems

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MDPI and ACS Style

Mesmouli, M.B.; Popa, I.-L.; Hassan, T.S. Existence and Stability Analysis of Nonlinear Systems with Hadamard Fractional Derivatives. Mathematics 2025, 13, 1869. https://doi.org/10.3390/math13111869

AMA Style

Mesmouli MB, Popa I-L, Hassan TS. Existence and Stability Analysis of Nonlinear Systems with Hadamard Fractional Derivatives. Mathematics. 2025; 13(11):1869. https://doi.org/10.3390/math13111869

Chicago/Turabian Style

Mesmouli, Mouataz Billah, Ioan-Lucian Popa, and Taher S. Hassan. 2025. "Existence and Stability Analysis of Nonlinear Systems with Hadamard Fractional Derivatives" Mathematics 13, no. 11: 1869. https://doi.org/10.3390/math13111869

APA Style

Mesmouli, M. B., Popa, I.-L., & Hassan, T. S. (2025). Existence and Stability Analysis of Nonlinear Systems with Hadamard Fractional Derivatives. Mathematics, 13(11), 1869. https://doi.org/10.3390/math13111869

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