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

2021/09/23 by Arzu Ahmadova, Ahmadova, Arzu, Nazım I. Mahmudov +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2109.11493

openalex publication_date 2021/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 α∈ ((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.

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