  In this paper we study the moderate deviations principle (MDP) for slow-fast
stochastic dynamical systems where the slow motion is governed by small
fractional Brownian motion (fBm) with Hurst parameter $H\in(1/2,1)$. We derive
conditions on the moderate deviations scaling and on the Hurst parameter $H$
under which the MDP holds. In addition, we show that in typical situations the
resulting action functional is discontinuous in $H$ at $H=1/2$, suggesting that
the tail behavior of stochastic dynamical systems perturbed by fBm can have
different characteristics than the tail behavior of such systems that are
perturbed by standard Brownian motion.
