Finite Time Stability Analysis for Fractional Stochastic Neutral Delay Differential Equations

In this manuscript, we delve into the study of a stochastic differential equation with a fractional order and a time delay, encompassing deterministic and stochastic components. Our primary aim is to rigorously establish the existence of a unique solution that follows specified initial conditions, achieved through mathematical analysis. Moreover, we extend our research to investigate the finite-time stability of the system, analyzing trajectory behavior within a specific time frame. Employing advanced mathematical techniques, we systematically verify the finite-time stability, providing insights into convergence and stability within this defined interval. By employing illustrative examples, we strengthen this all-encompassing investigation into the intricate dynamics and stability properties that exist in fractionally ordered stochastic systems with time delays.