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A variation of constant formula for Caputo fractional stochastic differential equations

Author

Listed:
  • Anh, P.T.
  • Doan, T.S.
  • Huong, P.T.

Abstract

We establish and prove a variation of constant formula for Caputo fractional stochastic differential equations whose coefficients satisfy a standard Lipschitz condition. The main ingredient in the proof is to use Ito’s representation theorem and the known variation of constant formula for deterministic Caputo fractional differential equations. As a consequence, for these systems we point out the coincidence between the notion of classical solutions introduced in Wang et al. (2016) and mild solutions introduced in Sakthivel et al. (2013).

Suggested Citation

  • Anh, P.T. & Doan, T.S. & Huong, P.T., 2019. "A variation of constant formula for Caputo fractional stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 351-358.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:351-358
    DOI: 10.1016/j.spl.2018.10.010
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    Citations

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    Cited by:

    1. James Hoult & Yubin Yan, 2024. "Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise," Mathematics, MDPI, vol. 12(3), pages 1-18, January.
    2. Lu, Ziqiang & Zhu, Yuanguo, 2022. "Nonlinear impulsive problems for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Huong, P.T. & The, N.T., 2023. "Well-posedness and regularity for solutions of Caputo stochastic fractional delay differential equations," Statistics & Probability Letters, Elsevier, vol. 195(C).
    4. Xu, Shuli & Feng, Yuqiang & Jiang, Jun & Nie, Na, 2022. "A variation of constant formula for Caputo fractional stochastic differential equations with jump–diffusion," Statistics & Probability Letters, Elsevier, vol. 185(C).
    5. Giacomo Ascione & Enrica Pirozzi, 2020. "On the Construction of Some Fractional Stochastic Gompertz Models," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
    6. Luo, Danfeng & Tian, Mengquan & Zhu, Quanxin, 2022. "Some results on finite-time stability of stochastic fractional-order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    7. 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).
    8. Enrica Pirozzi, 2024. "Mittag–Leffler Fractional Stochastic Integrals and Processes with Applications," Mathematics, MDPI, vol. 12(19), pages 1-20, October.

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