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

Author name : Fahad Mohammed Alsharari
Publication Date : 2024-12-27
Journal Name : Fractal Fract. -MDPI

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

Publication Link

https://doi.org/10.3390/fractalfract9010007

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