Abstract
In this paper, we present a class of stochastic system of fractional space diffusion equations forced by additive noise. Our goal here is to approximate the solutions of this system via a system of ordinary differential equations. Moreover, we study the influence of the same degenerate additive noise on the stability of the solutions of the stochastic system of fractional diffusion equations. We are interested in the systems that have nonlinear polynomial and give applications as Lotka-Volterra system from biology and the Brusselator model for the Belousov-Zhabotinsky chemical reaction from chemistry to illustrate our results.