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On the Existence and Uniqueness of Solutions for Multidimensional Fractional Stochastic Differential Equations with Variable Order

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  • Seyfeddine Moualkia

    (School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China
    Department of Mathematics, 8 Mai 1945-Guelma University, Guelma 24000, Algeria)

  • Yong Xu

    (School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China)

Abstract

Fractional stochastic differential equations are still in their infancy. Based on some existing results, the main difficulties here are how to deal with those equations if the fractional order is varying with time and how to confirm the existence of their solutions in this case. This paper is about the existence and uniqueness of solutions to the fractional stochastic differential equations with variable order. We prove the existence by using the Picard iterations and propose new sufficient conditions for the uniqueness.

Suggested Citation

  • Seyfeddine Moualkia & Yong Xu, 2021. "On the Existence and Uniqueness of Solutions for Multidimensional Fractional Stochastic Differential Equations with Variable Order," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2106-:d:626395
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    References listed on IDEAS

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    1. Ahmadova, Arzu & Mahmudov, Nazim I., 2020. "Existence and uniqueness results for a class of fractional stochastic neutral differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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    Cited by:

    1. Moualkia, Seyfeddine, 2023. "Mathematical analysis of new variant Omicron model driven by Lévy noise and with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Moualkia, Seyfeddine & Liu, Yang & Qiu, Jianlong & Lu, Jianquan, 2024. "An averaging result for fractional variable-order neutral differential equations with variable delays driven by Markovian switching and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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