Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics

We revisit the Mittag-Leffler functions of a real variable $t$, with one, two and three order-parameters $\{\alpha ,\beta ,\gamma \}$, as far as their Laplace transform pairs and complete monotonicty properties are concerned. These functions, subjected to the requirement to be completely monotone for $t>0$, are shown to be suitable models for non–Debye relaxation phenomena in dielectrics including as particular cases the classical models referred to as Cole-Cole, Davidson-Cole and Havriliak-Negami. We show 3D plots of the response functions and of the corresponding spectral distributions, keeping fixed one of the three order-parameters.