We analyze an anisotropic fractional diffusion equation that extends some known diffusion equations by considering a diffusion coefficient with spatial and time dependence, the presence of external forces and time fractional derivatives. We obtain new exact classes of solutions for a linear...

A continuous time random walk model is presented with long-tailed waiting time density that approaches a Gaussian distribution in the continuum limit. This example shows that continuous time random walks with long time tails and diffusion equations with a fractional time derivative are in...

It is well known that Brownian diffusion is characterized by a mean-squared displacement which varies linearly in time, 〈r2〉∼t and that anomalous diffusion, by a mean-square displacement which is nonlinear in time, 〈r2〉∼tα. It is generally accepted that fractional diffusion, which...