On the averaging principle for stochastic differential equations involving Caputo fractional derivative.

In this paper, we investigate the averaging principle for Caputo-type fractional stochastic differential equations driven by Brownian motion. Different from the approach of integration by parts or decomposing integral interval to deal with the estimation of integral involving singular kernel in the existing literature, we show the desired averaging principle in the sense of mean square by using Hölder inequality via growth conditions on the nonlinear stochastic term. Finally, a simulation example is given to verify the theoretical results.