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Ulam–Hyers stability for an impulsive Caputo–Hadamard fractional neutral stochastic differential equations with infinite delay

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  • Rhaima, Mohamed

Abstract

This paper addresses existence and Ulam–Hyers stability (UHS) problems for an impulsive Caputo–Hadamard fractional neutral functional stochastic differential equation with infinite delay (FNFSDEwID). We first prove the existence and uniqueness of the solution using Banach fixed point theorem and standard stochastic analysis techniques. We then tackle the UHS under a Lipschitz condition on a bounded and closed interval. We end up with an illustrative example that corroborates our theoretical findings.

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  • 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.
    • Handle: RePEc:eee:matcom:v:210:y:2023:i:c:p:281-295
    DOI: 10.1016/j.matcom.2023.03.020
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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. 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).
    3. 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).
    4. Khan, Aziz & Khan, Hasib & Gómez-Aguilar, J.F. & Abdeljawad, Thabet, 2019. "Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 422-427.
    5. Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    6. Abdeljawad, Thabet & Atangana, Abdon & Gómez-Aguilar, J.F. & Jarad, Fahd, 2019. "On a more general fractional integration by parts formulae and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
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