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Mean-square asymptotic stability of fractional-order nonlinear stochastic dynamic system

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Abstract

In this paper, the mean-square asymptotic stability problem is investigated for the fractional-order nonlinear stochastic dynamic system in Hilbert space. First, a set of sufficient stability conditions based on the Mittag–Leffler function is established to achieve the mean-square asymptotic stability of the system under the Lipschitz condition and linear growth condition, respectively. Next, the convergence analysis of the closed-loop system is finished by directly utilizing the properties of the integral solution and Mittag–Leffler function. Furthermore, in Euclidean space, the mean-square asymptotic stability problem is addressed for the fractional-order nonlinear stochastic dynamic system, in which sufficient stability conditions are given based on the eigenvalues of the matrix operator. Finally, two numerical examples are performed to verify the correctness of the proposed theoretical results.

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Data availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors gratefully acknowledge partial financial support from the National Natural Science Foundation of China (Grant Nos. 62003026, 62173027 and 61973329), and the Natural Science Foundation of Beijing Municipality (Grant No. Z180005).

Funding

This work is supported in part by the National Natural Science Foundation of China (Grant Nos. 62003026, 62173027 and 61973329), and the Natural Science Foundation of Beijing Municipality (Grant No. Z180005).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Xiaolin Yuan, Yongguang Yu, Zhenzhen Lu & Guojian Ren

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  1. Xiaolin Yuan
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  2. Yongguang Yu
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  3. Zhenzhen Lu
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  4. Guojian Ren
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Contributions

All authors contributed to the study, conception, and design. Analysis was performed by XY, YY, ZL and GR. The first draft of the manuscript was written by XY and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Guojian Ren.

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Yuan, X., Yu, Y., Lu, Z. et al. Mean-square asymptotic stability of fractional-order nonlinear stochastic dynamic system. Nonlinear Dyn 111, 985–996 (2023). https://doi.org/10.1007/s11071-022-07994-3

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