Anomalous relaxation in dielectrics with Hilfer fractional derivative

Autor:	Plata, A. R. Gomez, Rosa, Ester C. A. F., Rodriguez-Giraldo, R. G, de Oliveira, E. Capelas
Rok vydání:	2020
Předmět:	Condensed Matter - Statistical Mechanics Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	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. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2001.06856 Zobrazit plný text záznamu View this record from Arxiv