MMN-3600

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

Arzu Ahmadova; Nazim I. Mahmudov;

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 \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.


Vol. 22 (2021), No. 2, pp. 503-520
DOI: https://doi.org/10.18514/MMN.2021.3600


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