Anomalous diffusion on fractal objects: additional analytic solutions

In this paper we present analytical calculations for the propagator p(r,t), the probability to reach a distance r at time t having started at the origin t=0, on a generalization of the Euclidean diffusion equation for diffusion on fractals. The results are confronted with exact analytical expressions. It is shown that the autocorrelation function P(0,t) scales according to p(0,t)≈t−ds/2. The results extend the previously derived expressions. Progress has been made in this direction by introducing the symmetries of the generalized diffusion equation.