The fractional diffusion equation that is constructed replacing the time derivative with a fractional derivative, (0)D(alpha)(t) f = C(alpha) theta(2) f/theta x(2), where (0)D(alpha)(t) is the Riemann-Liouville derivative operator, is characterized by a probability density that decays with time as t(alpha -1) (alpha < 1) and an initial condition that diverges as t -->0 [R. Hilfer, J. Phys. Chem...

In this article we give a general prescription for incorporating memory effects in phase space kinetic equation, and consider in particular the generalized "fractional" relaxation time model equation. We solve this for small-signal charge carriers undergoing scattering, trapping, and detrapping in a time-of-flight experimental arrangement in two ways: (i) approximately via the Chapman-Enskog sc...

Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of ...