Studying the Stability of the ψ-Hilfer Fractional Differential System
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 t...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/5437691 |
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| _version_ | 1850231009039089664 |
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| author | Jinping Yang Zhiqiang Li |
| author_facet | Jinping Yang Zhiqiang Li |
| author_sort | Jinping Yang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0663e56a1d3d4d6f89b9d7d3f0bd0c71 |
| institution | OA Journals |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-0663e56a1d3d4d6f89b9d7d3f0bd0c712025-08-20T02:03:40ZengWileyComplexity1099-05262022-01-01202210.1155/2022/5437691Studying the Stability of the ψ-Hilfer Fractional Differential SystemJinping Yang0Zhiqiang Li1Department of MathematicsDepartment of MathematicsThis 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.http://dx.doi.org/10.1155/2022/5437691 |
| spellingShingle | Jinping Yang Zhiqiang Li Studying the Stability of the ψ-Hilfer Fractional Differential System Complexity |
| title | Studying the Stability of the ψ-Hilfer Fractional Differential System |
| title_full | Studying the Stability of the ψ-Hilfer Fractional Differential System |
| title_fullStr | Studying the Stability of the ψ-Hilfer Fractional Differential System |
| title_full_unstemmed | Studying the Stability of the ψ-Hilfer Fractional Differential System |
| title_short | Studying the Stability of the ψ-Hilfer Fractional Differential System |
| title_sort | studying the stability of the ψ hilfer fractional differential system |
| url | http://dx.doi.org/10.1155/2022/5437691 |
| work_keys_str_mv | AT jinpingyang studyingthestabilityofthepshilferfractionaldifferentialsystem AT zhiqiangli studyingthestabilityofthepshilferfractionaldifferentialsystem |