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 |
| Published: |
Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/5437691 |
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| Summary: | 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. |
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| ISSN: | 1099-0526 |