Physical meaning of the stretched exponential Kohlrausch function

In this paper the physical meaning of the empirical Kohlrausch-Williams-Watts (KWW) function is explained in terms of the linear oscillator theory. It is shown that the KWW function is a solution of the non-autonomous linear first order equation for an overdamped linear oscillator. From the linear oscillator model it follows that the KWW-type relaxation is the linear relaxation with a time (coordinate, stress, voltage, etc.) dependent dissipation of energy. The theoretical results are validated by measurements. A method for modeling KWW-type relaxation using simple electrical circuits is proposed.