An Application of Fractional Calculus to Dielectric Relaxation Processes

Abstract

Recently fractional calculus has been successfully applied in the description of complex dynamics and proved to be a valuable tool for the solution of non-linear differential equations. In this study, an autocorrelation function obtained from the one-dimensional stochastic Ising model is assumed to be identical to the dipole correlation function of a molecular chain, and the fractional calculus method is applied to obtain a fractional diffusion equation derived from the stochastic Ising model applicable to the dielectric relaxation processes observed in polar materials. The equation is solved by using the Adomian decomposition method. At low temperatures, the solution of the equation is found to be compatible with the Cole–Cole and KWW (Kohlrausch–William–Watts) equations, and also with the algebraic decay relaxation function. Copyright © 2002 IFAC.