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Sufficient Conditions for Optimal Stability in Hilfer–Hadamard Fractional Differential Equations

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  • Safoura Rezaei Aderyani

    (School of Mathematics and Computer Science, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran)

  • Reza Saadati

    (School of Mathematics and Computer Science, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran)

  • Donal O’Regan

    (School of Mathematical and Statistical Sciences, University of Galway, H91 TK33 Galway, Ireland)

Abstract

The primary objective of this study is to explore sufficient conditions for the existence, uniqueness, and optimal stability of positive solutions to a finite system of Hilfer–Hadamard fractional differential equations with two-point boundary conditions. Our analysis centers around transforming fractional differential equations into fractional integral equations under minimal requirements. This investigation employs several well-known special control functions, including the Mittag–Leffler function, the Wright function, and the hypergeometric function. The results are obtained by constructing upper and lower control functions for nonlinear expressions without any monotonous conditions, utilizing fixed point theorems, such as Banach and Schauder, and applying techniques from nonlinear functional analysis. To demonstrate the practical implications of the theoretical findings, a pertinent example is provided, which validates the results obtained.

Suggested Citation

  • Safoura Rezaei Aderyani & Reza Saadati & Donal O’Regan, 2025. "Sufficient Conditions for Optimal Stability in Hilfer–Hadamard Fractional Differential Equations," Mathematics, MDPI, vol. 13(9), pages 1-22, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1525-:d:1650024
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    References listed on IDEAS

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    1. Constantinos Challoumis, 2024. "Integrating Money Cycle Dynamics and Economocracy for Optimal Resource Allocation and Economic Stability," JRFM, MDPI, vol. 17(9), pages 1-25, September.
    2. Almalahi, Mohammed A. & Panchal, Satish K. & Jarad, Fahd, 2021. "Stability results of positive solutions for a system of ψ -Hilfer fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Santanu Saha Ray & Abdon Atangana & S. C. Oukouomi Noutchie & Muhammet Kurulay & Necdet Bildik & Adem Kilicman, 2014. "Fractional Calculus and Its Applications in Applied Mathematics and Other Sciences," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-2, December.
    4. Margarita Rivero & Sergei V. Rogosin & José A. Tenreiro Machado & Juan J. Trujillo, 2013. "Stability of Fractional Order Systems," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-14, May.
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