Riemann–Liouville Fractional Stochastic Neutral Integro‐Differential Systems

ABSTRACT This paper presents novel results on the asymptotic stability of mild solutions in the th moment for Riemann–Liouville fractional stochastic neutral integro‐differential systems (abbreviated as Riemann–Liouville FSNIDSs) of order , using Banach's contraction mapping principle. The central contribution lies in deriving the mild solution of FSNIDSs with a Riemann–Liouville fractional time derivative by applying a stochastic version of the. variation of constants formula. The analysis draws upon the theory of fractional differential equations, properties of Mittag‐Leffler functions, and techniques from asymptotic analysis, under the assumption that the corresponding fractional stochastic neutral dynamical system is asymptotically stable.