Ulam–Hyers Stability for a Class of Hilfer-Type Fractional Stochastic Differential Equations

Abstract

In this work, we study a class of Hilfer-type fractional stochastic differential equations (HFSDEs). By Laplace transform and its inverse, we obtain a mild solution to HFSDEs. Furthermore, we research the existence and uniqueness of solutions to the addressed equations. Subsequently, we explore the Ulam–Hyers (U–H) stability of the considered system by the Picard iteration. Finally, we verify the correctness of the theoretical results with an example.