Ulam-Hyers Stability for a Class of Caputo-Type Fractional Stochastic System with Delays

In this study, we explore the Caputo-type fractional stochastic differential equations (FSDEs) with delays. Firstly, the existence and uniqueness of the solutions for the considered system are obtained under the non-Lipschitz condition by using the Caratheodory approximation method with the aid of Fatous Lemma, Ito isometry, Cauchy-Schwarz inequality, and Gronwall's inequality. Secondly, we study the Ulam-Hyers (U-H) stability of the addressed equations with the aid of the Cauchy-Schwarz inequality and Gronwall's inequality. Finally, an example with numerical simulation is presented to support the validity of our theory.