Studying the Stability of the ψ-Hilfer Fractional Differential System

Jinping Yang, Zhiqiang Li and Abdellatif Ben Makhlouf

Complexity, 2022, vol. 2022, 1-18

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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:5437691

DOI: 10.1155/2022/5437691

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