Asymptotic stability analysis of Riemann-Liouville fractional stochastic neutral differential equations

[摘要] The novelty of our paper is to establish results on asymptotic stability of mild solutions in pth moment to Riemann-Liouville fractional stochastic neutral differential equations (for short Riemann-Liouville FSNDEs) of order \alpha in (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 differential equation system is asymptotically stable.

[学科分类] 数学（综合）

[关键词] Riemann-Liouville fractional derivative;fractional stochastic neutral dynamical systems;existence and uniqueness;asymptotic stability;continuity of mild solutions in pth moment