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Accelerating and retarding anomalous diffusion. (English) Zbl 1237.35166
Summary: 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 long-time 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.
MSC:
35R60PDEs with randomness, stochastic PDE
35R11Fractional partial differential equations
60G15Gaussian processes
60J60Diffusion processes