Studying the Stability of the ψ-Hilfer Fractional Differential System. (16th July 2022)

• Record Type: Journal Article
• Authors: Yang, Jinping; Li, Zhiqiang
• Other Names: Ben Makhlouf Abdellatif Academic Editor.
• Is Part Of: Complexity. Volume 2022(2022)
• Publication Date: 2022-07-16
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2022/5437691
• Languages: English
• ISSNs: 1076-2787

Abstract

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.