Anomalous Relaxation in the Fractal Time Random Walk Model

We study relaxation properties of the fractal time random walk model in which the waiting time distribution is given by the power law type t^-1-a. By means of theoretical analyses as well as of Monte Carlo simulations of this model, we find that the relaxation becomes anomalous in the case of $a<1$ where the complex susceptibility is described by the Cole-Cole form. On the other hand, the normal Debye type relaxation is observed for $a>1$. We also find the scaling laws both for the relaxation function and for the particle density.