Ulam–Hyers Stability of Caputo‐Type Fractional Stochastic Differential Equations with Time Delays
X Wang, D Luo, Z Luo, A Zada - Mathematical Problems in …, 2021 - Wiley Online Library
X Wang, D Luo, Z Luo, A Zada
Mathematical Problems in Engineering, 2021•Wiley Online LibraryIn 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 e´ odory approximation. Furthermore, with the help of H o¨
lder's inequality, Jensen's inequality, It o∧ 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 …
(FSDEs) with time delays. Under some new criteria, we get the existence and uniqueness of
solutions to FSDEs by Carath e´ odory approximation. Furthermore, with the help of H o¨
lder's inequality, Jensen's inequality, It o∧ 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 …
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 Carathodory approximation. Furthermore, with the help of Hlder’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.