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Ulam–Hyers Stability of Caputo-Type Fractional Stochastic Differential Equations with Time Delays

Author

Listed:
  • Xue Wang
  • Danfeng Luo
  • Zhiguo Luo
  • Akbar Zada

Abstract

In this paper, we study a class of Caputo-type fractional stochastic differential equations (FSDEs) with time delays. Under some new criteria, we get the existence and uniqueness of solutions to FSDEs by Carath odory approximation. Furthermore, with the help of H lder’s inequality, Jensen’s inequality, It isometry, and Gronwall’s inequality, the Ulam–Hyers stability of the considered system is investigated by using Lipschitz condition and non-Lipschitz condition, respectively. As an application, we give two representative examples to show the validity of our theories.

Suggested Citation

  • Xue Wang & Danfeng Luo & Zhiguo Luo & Akbar Zada, 2021. "Ulam–Hyers Stability of Caputo-Type Fractional Stochastic Differential Equations with Time Delays," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-24, March.
    • Handle: RePEc:hin:jnlmpe:5599206
    DOI: 10.1155/2021/5599206
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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. Abdelhamid Mohammed Djaouti & Zareen A. Khan & Muhammad Imran Liaqat & Ashraf Al-Quran, 2024. "Existence, Uniqueness, and Averaging Principle of Fractional Neutral Stochastic Differential Equations in the L p Space with the Framework of the Ψ-Caputo Derivative," Mathematics, MDPI, vol. 12(7), pages 1-21, March.

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