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Studying the Stability of the ψ‐Hilfer Fractional Differential System

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  • Jinping Yang
  • Zhiqiang Li

Abstract

This paper devotes to the study on the stability and decay of solution to fractional differential system involving the ψ‐Hilfer fractional derivative of order α ∈ (0,1) and type β ∈ [0,1]. We first derive the solution of linear system by using the generalized Laplace transform, which can be represented by the form of Mittag‐Leffler function. Then, in terms of the asymptotic expansion of the Mittag‐Leffler function, stability properties of linear system are analyzed in more detail. Finally, we construct a linearization theorem and determine the stability near the equilibrium for the autonomous nonlinear differential system with the ψ‐Hilfer derivative.

Suggested Citation

  • Jinping Yang & Zhiqiang Li, 2022. "Studying the Stability of the ψ‐Hilfer Fractional Differential System," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:5437691
    DOI: 10.1155/2022/5437691
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    References listed on IDEAS

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    1. Oana Brandibur & Roberto Garrappa & Eva Kaslik, 2021. "Stability of Systems of Fractional-Order Differential Equations with Caputo Derivatives," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    2. Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2021. "Stability Concepts of Riemann-Liouville Fractional-Order Delay Nonlinear Systems," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
    3. Muath Awadalla & Abdellatif Ben Makhlouf, 2022. "Some Existence Results for a System of Nonlinear Sequential Fractional Differential Equations with Coupled Nonseparated Boundary Conditions," Complexity, Hindawi, vol. 2022, pages 1-17, February.
    4. Muath Awadalla, 2022. "Some Existence Results for a System of Nonlinear Sequential Fractional Differential Equations with Coupled Nonseparated Boundary Conditions," Complexity, John Wiley & Sons, vol. 2022(1).
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