Abstract
In the framework of the one-dimensional fractal time random walk (FTRW) relaxation model, we rigorously show that the frequency domain response 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) determined in this model by the Mittag-Leffler distribution. We provide also analytical formulas for the propagators of the nonbiased and biased FTRWs.
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