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Studying the Stability of the ψ-Hilfer Fractional Differential System

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  • Jinping Yang
  • Zhiqiang Li
  • Abdellatif Ben Makhlouf

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 & Abdellatif Ben Makhlouf, 2022. "Studying the Stability of the ψ-Hilfer Fractional Differential System," Complexity, Hindawi, vol. 2022, pages 1-18, July.
    • Handle: RePEc:hin:complx:5437691
    DOI: 10.1155/2022/5437691
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