MMN-3600

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

• Arzu Ahmadova, Eastern Mediterranean University, Department of Mathematics, Famagusta, 99628 T. R. Northen Cyprus, Mersin 10 Turkey, arzu.ahmadova@emu.edu.tr
• Nazim I. Mahmudov, Eastern Mediterranean University, Department of Mathematics, Famagusta, 99628 T. R. Northen Cyprus, Mersin 10 Turkey, nazim.mahmudov@emu.edu.tr

## 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: 10.18514/MMN.2021.3600