Some Existence, Uniqueness, and Stability Results for a Class of ϑ-Fractional Stochastic Integral Equations

Abstract

This paper focuses on the existence and uniqueness of solutions for ϑ-fractional stochastic integral equations (ϑ-FSIEs) using the Banach fixed point theorem (BFPT). We explore the Ulam–Hyers stability (UHS) of ϑ-FSIEs through traditional methods of stochastic calculus and the BFPT. Moreover, the continuous dependence of solutions on initial conditions is proven. Additionally, we provide three examples to demonstrate our findings.