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.
Keywords
fractional integral with respect to another function; stochastic calculus; Ulam–Hyers stability