Anomalous relaxation in dielectrics with Hilfer fractional derivative

A. R. Gomez Plata, Ester C. A. F. Rosa, R. G Rodriguez-Giraldo, E. Capelas de Oliveira

Published 2020-01-19Version 1

We introduce a new relaxation function depending on an arbitrary parameter as solution of a kinetic equation in the same way as the relaxation function introduced empirically by Debye, Cole-Cole, Davidson-Cole and Havriliak-Negami, anomalous relaxation in dielectrics, which are recovered as particular cases. We propose a differential equation introducing a fractional operator written in terms of the Hilfer fractional derivative of order {\xi}, with 0<{\xi}<1 and type {\eta}, with 0<{\eta}<1. To discuss the solution of the fractional differential equation, the methodology of Laplace transform is required. As a by product we mention particular cases where the solution is completely monotone. Finally, the empirical models are recovered as particular cases.