Analytic physical model of anisotropic anomalous diffusion

The temporal Fokker-Planck equation is analytically integrated in an arbitrary number of spatial dimensions but with the 2D and 3D results highlighted. It is shown that a temporal power-law ansatz for the anisotropic diffusion coefficients leads naturally to a physically reasonable model of normal and anomalous diffusion with drift. An interpretation of the drift and diffusion coefficients is provided and the analytic growth rate of the area and volume of uncertainty is determined. It is shown that the asymptotic growth of the uncertainty in the volume of space about the mean position is proportional to the square-root of time raised to the power of the sum over all exponents of the anisotropic diffusion coefficients.