Defect diffusion approach to dielectric relaxation with fractional probability distribution

In this study, some approaches had carried out to describe the relaxation processes of dielectric systems with chain molecule. For this purpose, Defect-Diffusion model, which is based on the assumption that a defect propagates randomly in one dimension and reaches molecule and causes its relaxation, is discussed. During the development of the model, Fractional calculus, which gained considerable importance in recent years and has been founded various application areas in many disciplines, was used. The mechanism of relaxation is investigated with various fractional probability distributions under the assumption that the probability distribution of the random walk in the system is in the fractional space. As a result, the relaxation functions corresponding to the empirical Cole-Cole, Cole-Davidson and Havrilik-Negami type behaviors were obtained. The results are used to explain the non-Debye behaviors of dielectrics.