Ulam–Hyers stability of Caputo–Hadamard fractional stochastic differential equations with time-delays and impulses

Abstract

In this article, a class of Caputo–Hadamard fractional stochastic differential equation (FSDEs) with time-delays and impulses is considered. With the help of contraction mapping principle, we derive the existence and uniqueness of the solutions to the purposed system. Subsequently, by virtue of the stochastic analysis techniques and generalized Gr\(\ddot{o}\)nwall inequality, the Ulam–Hyers stability (U–Hs) of the addressed system is established. Finally, we present an example to illustrate the theoretical results.