Finite-time stability of nonlinear stochastic $ \psi $-Hilfer fractional systems with time delay

Qing Yang; Chuanzhi Bai; Dandan Yang; Qing Yang; Chuanzhi Bai; Dandan Yang

doi:10.3934/math.20221037

AIMS Mathematics

2022, Volume 7, Issue 10: 18837-18852. doi: 10.3934/math.20221037

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Research article

Finite-time stability of nonlinear stochastic $ \psi $-Hilfer fractional systems with time delay

Department of Mathematics, Huaiyin Normal University, Huaian, Jiangsu 223300, China

Received: 19 July 2022 Revised: 15 August 2022 Accepted: 18 August 2022 Published: 25 August 2022
MSC : 26A33, 34A08, 34D20, 34F05, 60J65

In this paper, we study the finite time stability of stochastic $ \psi $-Hilfer fractional-order time-delay systems. Under the stochastic analysis techniques and the generalized Gronwall's inequality for $ \psi $-fractional derivative, the criterion of finite time stability of the solution for nonlinear stochastic $ \psi $-Hilfer fractional systems with time delay is obtained. An example is provided to illustrate the effectiveness of the proposed methods. Some known results in the literature are extended.
- $ \psi $-Hilfer fractional derivative,
- generalized Gronwall's inequality,
- finite time stability
Citation: Qing Yang, Chuanzhi Bai, Dandan Yang. Finite-time stability of nonlinear stochastic $ \psi $-Hilfer fractional systems with time delay[J]. AIMS Mathematics, 2022, 7(10): 18837-18852. doi: 10.3934/math.20221037

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Abstract

In this paper, we study the finite time stability of stochastic $ \psi $-Hilfer fractional-order time-delay systems. Under the stochastic analysis techniques and the generalized Gronwall's inequality for $ \psi $-fractional derivative, the criterion of finite time stability of the solution for nonlinear stochastic $ \psi $-Hilfer fractional systems with time delay is obtained. An example is provided to illustrate the effectiveness of the proposed methods. Some known results in the literature are extended.

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