We establish a slow manifold for a fast-slow dynamical system with anomalous diffusion,where both fast and slow components are influenced by white noise.Furthermore,we verify the exponential tracking property for the established random slow manifold,which leads to a lower dimensional reduced system.Alongside this we consider a parameter esti-mation method for a nonlocal fast-slow stochastic dynamical system,where only the slow component is observable.In terms of quantifying parameters in stochastic evolutionary sys-tems,the provided method offers the advantage of dimension reduction.