Relaxation Processes and Fractional Differential Equations

Abstract

Relaxation properties of different media (dielectrics, semiconductors, ferromagnetics, and so on) are normally expressed in terms of response function f(t) or of real and imaginary components of its Fourier transform dependent on the frequency ω. It had been recently recognized that most of real materials show deviation from classical Debye process. There exist a few empirical approximations of non-Debye response functions. One of them is the two-power approximation containing ωα and ωβ, where α and β belong to the interval (0, 1). This formula gives the basis for introducing of fractional differential equation considered in this paper. A stochastic interpretation of this equation is offered; its solution is found and investigated. The results are in agreement with experimental data.