Analysis of Neutral Stochastic Fractional Differential Equations Involving Riemann–Liouville Fractional Derivative with Retarded and Advanced Arguments

This typescript explores the existence and uniqueness of solutions for Riemann–Liouville neutral stochastic fractional differential equations with both retarded and advanced arguments. In order to establish the existence of solution, we applied the Mo´\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\acute{o}$$\end{document}ach condition, while for uniqueness, we utilized the Banach contraction principle. Furthermore, we studied the Hyers–Ulam stability of these equations. To reinforce our findings, we provide an example at the conclusion of the manuscript.