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Existence and Stability Analysis of Nonlinear Systems with Hadamard Fractional Derivatives

Author

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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
    Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania)

  • Taher S. Hassan

    (Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

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.

Suggested Citation

  • Mouataz Billah Mesmouli & Ioan-Lucian Popa & Taher S. Hassan, 2025. "Existence and Stability Analysis of Nonlinear Systems with Hadamard Fractional Derivatives," Mathematics, MDPI, vol. 13(11), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1869-:d:1671038
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    References listed on IDEAS

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    1. Ghanbari, Behzad & Günerhan, Hatıra & Srivastava, H.M., 2020. "An application of the Atangana-Baleanu fractional derivative in mathematical biology: A three-species predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Ahmed Refice & Mohammed Said Souid & Ivanka Stamova, 2021. "On the Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order via Kuratowski MNC Technique," Mathematics, MDPI, vol. 9(10), pages 1-16, May.
    3. Mouataz Billah Mesmouli & Loredana Florentina Iambor & Amir Abdel Menaem & Taher S. Hassan, 2024. "Existence Results and Finite-Time Stability of a Fractional ( p , q )-Integro-Difference System," Mathematics, MDPI, vol. 12(9), pages 1-12, May.
    4. Roberto Garra & Enzo Orsingher & Federico Polito, 2018. "A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability," Mathematics, MDPI, vol. 6(1), pages 1-10, January.
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