ON THE COLE-COLE RELAXATION FUNCTION AND RELATED MITTAG-LEFFLER DISTRIBUTION

In the framework of the one-dimensional fractal time random walk (FTRW ) relaxation model, we rigorously show that the frequency domain respo nse takes, in both nonbiased and biased walks, the only possible Cole- Cole form. The underlying reason for this is the specific form of the relaxation function (the survival probability of a relaxing system) de termined in this model by the Mittag-Leffler distribution. We provide also analytical formulas for the propagators of the nonbiased and bias ed FTRWs.