Stochastic averaging for a type of fractional differential equations with multiplicative fractional Brownian motion.

This paper focuses on the averaging principle of Caputo fractional stochastic differential equations (SDEs) with multiplicative fractional Brownian motion (fBm), where Hurst parameter 1/2<H<1 and the integral of fBm as a generalized Riemann-Stieltjes integral. Under suitable assumptions, the averaging principle on Hölder continuous space is established by giving the estimate of Hölder norm. Specifically, we show that the solution of the original fractional SDEs converges to the solution of the proposed averaged fractional SDEs in the mean square sense and gives an example to illustrate our result.