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Averaging principle for stochastic Caputo fractional differential equations with non-Lipschitz condition

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Abstract

In this paper, the averaging principle for stochastic Caputo fractional differential equations (SCFDEs) with the nonlinear terms satisfying the non-Lipschitz condition is considered. The work in the article is roughly divided into three parts. Firstly, we establish a generalized Gronwall inequality with singular integral kernel which is a key part in our analysis. Secondly, we discuss the existence and uniqueness of solution. Finally, the averaging principle is considered.

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Acknowledgements

Zhongkai Guo was partly supported by the NSF of China (Grant Nos. 11926322), and “the Fundamental Research Funds for the Central Universities", South-Central MinZu University (Grant Number: CZY22013; 3212023sycxjj001). Junhao Hu was partially supported by the National Natural Science Foundation of China (Grant Nos. 62373383). The authors thank the reviewers for their valuable comments and kind suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, South-Central Minzu University, Wuhan, 430074, China

    Zhongkai Guo & Junhao Hu

  2. Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, AL, 36849, USA

    Xiaoying Han

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  1. Zhongkai Guo
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  2. Xiaoying Han
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  3. Junhao Hu
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Correspondence to Junhao Hu.

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Guo, Z., Han, X. & Hu, J. Averaging principle for stochastic Caputo fractional differential equations with non-Lipschitz condition. Fract Calc Appl Anal (2023). https://doi.org/10.1007/s13540-023-00211-x

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