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

TL;DR

This paper establishes the asymptotic stability of mild solutions in the p-th moment for Riemann-Liouville fractional stochastic neutral differential equations of order between 0.5 and 1, using a contraction mapping approach.

Contribution

It introduces a novel method to analyze the asymptotic stability of solutions to Riemann-Liouville fractional stochastic neutral differential equations employing the stochastic variation of constants formula.

Findings

Proves asymptotic stability of solutions under certain conditions.

Derives mild solutions using fractional variation of constants.

Utilizes Mittag-Leffler functions and fractional differential equations theory.

Abstract

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.