Time-domain simulation for fractional relaxation of Havriliak-Negami type

Abstract

The time-simulation of models described by the Havriliak-Negami response function is a challenging problem due to the absence of an explicit formulation for the corresponding differential operator in the time-domain. In this work, we discuss a convolution quadrature rule with convolution weights evaluated on the basis of the representation of the response function in the Laplace transform domain. We describe a general and straightforward technique for the computation of the weights and we present some numerical experiments to illustrate the effectiveness of the proposed approach.

Fractional Relaxation and Fractional Oscillation Models Involving Erdélyi-Kober Integrals

“…Non-Debye relaxation phenomena in dielectrics are often modeled by means of fractional differential equations that generalize the classical relaxation equation. In this framework, Mittag-Leffler-type functions play a relevant role to describe anomalous relaxation, including special cases such as the Cole-Cole [4], the Davidson-Cole [6], and the Havriliak-Negami [16,12] models (see also [17] for a short review about analytical representations of relaxation functions in non-Debye processes). In recent theoretical investigations [3,11], the authors studied fractional relaxation models with time-varying coefficients resorting to different approaches.…”

A phenomenological approach to anomalous transport in complex or disordered media

“…The anomalous transport in complex or disordered media involving amorphous semiconductors and insulators is governed by some nonlinear and nonlocal processes corresponding to analytically derived Debye and semi-empirical Cole-Cole(CC), Cole-Davidson(CD) and Havriliak-Negami(HN) type conductivity equations [34][35][36][37][38]. HN type conductivity equation may be derived analytically through using the mathematical instruments and approaches of the stochastic and fractional dynamics and this sheds light on the types of anomalous behaviors that occurred in the conductivity process.…”