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

Xue Wang, Danfeng Luo, Zhiguo Luo and Akbar Zada

Mathematical Problems in Engineering, 2021, vol. 2021, 1-24

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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:5599206

DOI: 10.1155/2021/5599206

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