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On the Averaging Principle of Caputo Type Neutral Fractional Stochastic Differential Equations

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Abstract

In this manuscript, we study the averaging principle for a class of neutral fractional stochastic differential equations. Firstly, the existence and uniqueness of solution are discussed by applying the principle of contraction mapping. Secondly, the averaging principle in the sense of \(L^{p}\) is studied by using the Jensen’s inequality, Hölder inequality, Burkholder–Davis–Gundy inequality, Grönwall–Bellman inequality and interval translation technique. In addition, we give an example and numerical simulations to analyze the theoretical results.

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Acknowledgements

The authors sincerely thank the editors and reviewers for their valuable time reviewing this manuscript and for their insightful comments.

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This work has been supported by the Natural Science Special Research Fund Project of Guizhou University (202002).

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  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China

    Jing Zou & Danfeng Luo

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  1. Jing Zou
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JZ: writing, review and editing, software, formal analysis. DL: review, supervision, funding acquisition.

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Correspondence to Danfeng Luo.

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Zou, J., Luo, D. On the Averaging Principle of Caputo Type Neutral Fractional Stochastic Differential Equations. Qual. Theory Dyn. Syst. 23, 82 (2024). https://doi.org/10.1007/s12346-023-00916-7

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