Ulam–Hyers stability for an impulsive Caputo–Hadamard fractional neutral stochastic differential equations with infinite delay

Abstract

This paper addresses existence and Ulam–Hyers stability (UHS) problems for an impulsive Caputo–Hadamard fractional neutral functional stochastic differential equation with infinite delay (FNFSDEwID). We first prove the existence and uniqueness of the solution using Banach fixed point theorem and standard stochastic analysis techniques. We then tackle the UHS under a Lipschitz condition on a bounded and closed interval. We end up with an illustrative example that corroborates our theoretical findings.