  We focus on fast-slow systems involving both fractional Brownian motion (fBm)
and standard Brownian motion (Bm). The integral with respect to Bm is the
standard Ito integral, and the integral with respect to fBm is the generalised
Riemann-Stieltjes integral using the tools of fractional calculus. An averaging
principle in which the fast-varying diffusion process of the fast-slow systems
acts as a noise to be averaged out in the limit is established. It is shown
that the slow process has a limit in the mean square sense, which is
characterized by the solution of stochastic differential equations driven by
fBm whose coefficients are averaged with respect to the stationary measure of
the fast-varying diffusion. The implication is that one can ignore the complex
original systems and concentrate on the averaged systems instead. This
averaging principle paves the way for reduction of computational complexity.
