  This paper investigates a non-autonomous slow-fast system, which is
generalized by stochastic differential equations (SDEs) with locally Lipschitz
coefficients, subjected to standard Brownian motion (Bm) and fractional
Brownian motion (fBm) with Hurst parameter 1/2<H<1. We concentrate on how to
handle both types of integrals with respect to Bm and fBm and the locally
Lispchitz continuity. The pathwise approach and the Ito stochastic calculus are
combined with the technique of stopping time to establish the averaging
principle where the averaged equation is defined. Then, the slow component of
the original slow-fast system converges to the solution of the proposed
averaged equation in the mean square sense is verified.
