An analysis of dielectric relaxation using the fractional master equation of the stochastic Ising model

Abstract

Abstract In this paper, we begin introducing some basic definitions and mathematical preliminaries of the fractional calculus theory. By using the fractional calculus technique (that is, calculus of derivatives and integrals of any arbitrary real or complex order) a solution of the fractional master equation derived from the stochastic Ising model of Glauber has been obtained and the result is applied to an analysis of the dielectric relaxation processes. From the solution of the equation, the Cole–Cole dispersion relation, KWW (Kohlrausch–William–Watts) equation and algebraic decay relaxation functions are obtained easily. Then these functions are compared with Bozdemir's earlier analysis of the stochastic Ising model.