Analysis of Drude model using fractional derivatives without singular kernels

Open Physics

Baleanu Dumitru¹  Jiménez Leonardo Martínez²  García J. Juan Rosales²  Contreras Abraham Ortega² 

[1] Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey;División de Ingenierías Campus Irapuato-Salamanca, Universidad de Guanajuato, Carretera Salamanca-Valle de Santiago, Salamanca, Guanajuato, México;

关键词: fractional calculus;    drude model;    caputo-fabrizio derivative;    atangana-baleanu derivative;    45.10.hj;    45.20.d;    66.70.df;   

DOI  :  10.1515/phys-2017-0073

来源: DOAJ

【 摘 要 】

We report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF), and fractional derivatives with a stretched Mittag-Leffler function. It is shown that the velocity and current density of electrons moving through a metal depend on both the time and the fractional order 0 < γ ≤ 1. Due to non-singular fractional kernels, it is possible to consider complete memory effects in the model, which appear neither in the ordinary model, nor in the fractional Drude model with Caputo fractional derivative. A comparison is also made between these two representations of the fractional derivatives, resulting a considered difference when γ < 0.8.

【 授权许可】

Unknown