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Some results on the study of Caputo–Hadamard fractional stochastic differential equations

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  • Ben Makhlouf, Abdellatif
  • Mchiri, Lassaad

Abstract

In this article, we show the existence and uniqueness of solution of Caputo–Hadamardfractional stochastic differential equations (CHFSDE) via the Banach fixed point method (BFPM). We analyze the Ulam–Hyers stability (UHS) of CHFSDE by the generalized and the classical Gronwall inequalities. Two examples are presented to illustrate our results.

Suggested Citation

  • Ben Makhlouf, Abdellatif & Mchiri, Lassaad, 2022. "Some results on the study of Caputo–Hadamard fractional stochastic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921011115
    DOI: 10.1016/j.chaos.2021.111757
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    References listed on IDEAS

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    1. Ahmadova, Arzu & Mahmudov, Nazim I., 2021. "Ulam–Hyers stability of Caputo type fractional stochastic neutral differential equations," Statistics & Probability Letters, Elsevier, vol. 168(C).
    2. Abbas, Saïd & Benchohra, Mouffak & Lazreg, Jamal-Eddine & Zhou, Yong, 2017. "A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 47-71.
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    Cited by:

    1. Rhaima, Mohamed, 2023. "Ulam–Hyers stability for an impulsive Caputo–Hadamard fractional neutral stochastic differential equations with infinite delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 281-295.
    2. Kahouli, Omar & Ben Makhlouf, Abdellatif & Mchiri, Lassaad & Rguigui, Hafedh, 2023. "Hyers–Ulam stability for a class of Hadamard fractional Itô–Doob stochastic integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Rhaima, Mohamed & Mchiri, Lassaad & Ben Makhlouf, Abdellatif & Ahmed, Hassen, 2024. "Ulam type stability for mixed Hadamard and Riemann–Liouville Fractional Stochastic Differential Equations," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. Zhiyuan Yuan & Luyao Wang & Wenchang He & Ning Cai & Jia Mu, 2024. "Fractional Neutral Integro-Differential Equations with Nonlocal Initial Conditions," Mathematics, MDPI, vol. 12(12), pages 1-14, June.

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