Relaxation processes and fractional differential equations (Q1812139)

Relaxation properties of different media are normally expressed in terms of the time-domain response function \(f(t)\), which represents the current flowing under the action of a step-function electric field, or of the frequency-dependent real and imaginary components of its Fourier transform. Most of real materials show deviation from classical Debye process. One of the few empirical approximations of non-Debye response functions is the two-power approximation containing \(\omega^\alpha\) and \(\omega^\beta\) where \(\alpha,\beta \in (0,1)\). Based on this formula the author has introduced a certain fractional differential equation. A stochastic interpretation of this equation is given. Its solution is found and investigated. Experimental results are in agreement with the theoretical ones.