  The novelty of our paper is to establish results on asymptotic stability of
mild solutions in $p$th moment to Riemann-Liouville fractional stochastic
neutral differential equations (for short Riemann-Liouville FSNDEs) of order
$\alpha \in (\frac{1}{2},1)$ using a Banach's contraction mapping principle.
The core point of this paper is to derive the mild solution of FSNDEs involving
Riemann-Liouville fractional time-derivative by applying the stochastic version
of variation of constants formula. The results are obtained with the help of
the theory of fractional differential equations, some properties of
Mittag-Leffler functions and asymptotic analysis under the assumption that the
corresponding fractional stochastic neutral dynamical system is asymptotically
stable.
