  In this manuscript, we investigate a fractional stochastic neutral
differential equation with time delay, which includes both deterministic and
stochastic components. Our primary objective is to rigorously prove the
existence of a unique solution that satisfies given initial conditions.
Furthermore, we extend our research to investigate the finite-time stability of
the system by examining trajectory behavior over a given period. We employ
advanced mathematical approaches to systematically prove finite-time stability,
providing insights on convergence and stability within the stated interval.
Using illustrative examples, we strengthen this all-encompassing examination
into the complicated dynamics and stability features of fractionally ordered
stochastic systems with time delays. The implications of our results extend to
various fields, such as control theory, engineering, and financial mathematics,
where understanding the stability of complex systems is crucial.
