On the Rajagopal relaxation-time distribution and its relationship to the Kohlrausch–Williams–Watts relaxation function

A detailed analysis of the relationship of the Kohlrausch–Williams–Watts relaxation function to its recently proposed approximation resulting from the Rajagopal log-relaxation-time distribution is presented. Our considerations are based on the interpretation of the relaxation function as a survival probability of the initial state of a relaxing system expressed by means of the weighted average of an exponential decay with respect to the distribution of the effective relaxation time. Such an interpretation of the relaxation function enforces certain framework of analysis in which the basic probabilistic rules have to be fulfilled. In our approach, to compare the properties of the relaxation function resulting from the Rajagopal relaxation-time distribution and the Kohlrausch–Williams–Watts relaxation function, we use the strict relationship of the latter to the one-sided stable relaxation-rate distribution.