Continuous-time random walks and the fractional diffusion equation

The average probability density P(r,t) of random walks on fractals is revisited within the continuous-time random walks formalism. Corrections to the accepted asymptotic stretched Gaussian decay of P(r,t) of the form r alpha are discussed. It is shown that P(r,t) obeys a diffusion equation with a fractional time derivative asymptotically, and predictions about the value of alpha are presented.