Two different frameworks of the relaxation phenomenon are considered to conduct a detailed analytical analysis on the relationship of the stretched exponential relaxation function and the relaxation function resulting from a certain log-relaxation-time density proposed by Rajagopal. In the first part the analytical comparison of these two functions in the purely heterogeneous picture is presented. The 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. In the second part a certain degree of intrinsic nonexponentiality is assumed which allows to show the stochastic scheme leading directly from the Rajagopal density to the stretched exponential relaxation response. In both approaches the strict connection of Rajagopal function and the one-sided stable density is shown.

PACS numbers: 77.22.Gm, 02.50.Cw, 02.30.Uu