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Experimental data collected to provide us with information on the course ofdielectric relaxation phenomena are got according to two distinct schemes: onecan measure either the time decay of depolarization current or use methods ofthe broadband dielectric spectroscopy. Both sets of data are usually fitted bytime or frequency dependent elementary functions which in turn may beanalytically transformed among themselves using the Laplace transform andcompared each other. This leads to the question on comparability of results gotusing just mentioned experimental procedures. If we would like to do that inthe time domain we have to go beyond widely accepted Kohlrausch-Williams-Wattsapproximation and get acquainted with description using the Mittag-Lefflerfunctions. To convince the reader that the latter is not difficult tounderstand we propose to look at the problem from the point of view of objectssitting in the heart of stochastic processes approach to relaxation. These arethe characteristic exponents which are read out from the standard non-Debyefrequency dependent patterns. Characteristic functions appear to be expressedin terms of elementary functions which asymptotic analysis is simple. Thisopens new possibility to compare behavior of functions used to describenon-Debye relaxations. Results of such done comparison are fully confirmed bycalculations which use the powerful apparatus of the Mittag-Leffler functions.

Non-Debye relaxations: The ups and downs of the stretched exponential vs Mittag-Leffler's matchings