Fractional stochastic functional differential equations with non-Lipschitz condition

This article investigates fractional stochastic functional differential equations (FSFDEs) with a non-Lipschitz condition. The analysis explores the boundedness of solutions. Within this framework, results on the existence and uniqueness of solutions are presented. Furthermore, we derive error estimates between the Picard approximate solutions $y^n(t),n\ge 1$, and the exact solution $y(t)$. Finally, it is demonstrated that the solutions exhibit mean square stability. To illustrate the applicability of the proposed theory, a detailed example is presented.