Accelerating and Retarding Anomalous Diffusion

In this paper, Gaussian models of retarded and accelerated anomalous diffusion are considered. Stochastic differential equations of fractional order driven by single or multiple fractional Gaussian noise terms are introduced to describe retarding and accelerating subdiffusion and superdiffusion. Short-and longtime asymptotic limits of the mean-squared displacement of the stochastic processes associated with the solutions of these equations are studied. Specific cases of these equations are shown to provide possible descriptions of retarding or accelerating anomalous diffusion.