Abstract
This paper addresses the existence of stability results for Ulam-Hyers (UHS) and Ulam-Hyers-Rassias (UHRS) in the setting of Caputo-Hadamard fractional functional stochastic differential equations with delay (FFSDEwD). We first prove existence and uniqueness using Banach fixed point theorem coupled with standard stochastic analysis techniques. Then, we deal with UHS and UHRS results of Caputo-Hadamard FFSDEwD through an application of Gronwall inequality. Our theoretical findings are corroborated with two numerical examples.