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

Xue Wang | Zendy; Danfeng Luo | Zendy; Zhiguo Luo | Zendy; Akbar Zada | Zendy

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

Author(s) -

Xue Wang,

Danfeng Luo,

Zhiguo Luo,

Akbar Zada

Publication year - 2021

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2021/5599206

Subject(s) - mathematics , uniqueness , lipschitz continuity , type (biology) , stability (learning theory) , stress (linguistics) , pure mathematics , mathematical analysis , computer science , speech recognition , ecology , machine learning , biology

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 Carathe odory approximation. Furthermore, with the help of H€ older’s inequality, Jensen’s inequality, Ito 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.

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