Latest revision as of 11:59, 20 July 2026

Abstract

This study explores the existence, uniqueness (EU), and Hyers-Ulam stability (HUS) for a class of weighted fractional Itô-Doob stochastic integral equations (WFIDSIEs). To establish these crucial properties, we utilize the Banach fixed-point theorem (BFPT) as a foundational tool, alongside a variety of essential mathematical inequalities. These inequalities offer valuable insights into the underlying structure and behavior of WFIDSIEs, particularly in the context of fractional and stochastic dynamics. By leveraging these techniques, we demonstrate the conditions under which solutions to these equations exist and are unique, as well as how small perturbations affect the stability of these solutions in the Hyers-Ulam sense. Our results contribute to a deeper understanding of the stability and solvability of WFIDSIEs, which are important in modeling complex systems exhibiting both stochasticity and memory effects. Additionally, these findings open avenues for further research into the robustness of solutions in fractional stochastic models across various applied disciplines, such as finance, engineering, and biology.OPEN ACCESS Received: 12/09/2025 Accepted: 11/11/2025 Published: 21/07/2026

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