  We establish a slow manifold for a fast-slow stochastic evolutionary system
with anomalous diffusion, where both fast and slow components are influ- enced
by white noise. Furthermore, we prove the exponential tracking property for the
random slow manifold and this leads to a lower dimensional reduced sys- tem
based on the slow manifold. Also we consider parameter estimation for this
nonlocal fast-slow stochastic dynamical system, where only the slow component
is observable. In quantifying parameters in stochastic evolutionary systems,
this offers an advantage of dimension reduction.
