Fractional diffusion equation on fractals: Three-dimensional case and scattering function

Abstract

A fractional equation for diffusion in isotropic and homogeneous fractal structures is discussed. It generalizes the fractional diffusion equation valid for d-dimensional Euclidean systems. The asymptotic behaviour of the probability density function is obtained exactly. Analytical expressions are derived for the scattering and relaxation functions, which can be studied by X-ray and neutron scattering experiments on fractals.