Fractional drude model of electrons in a metal

Abstract

In the present work we analyse the behaviour of electrons in a metal placed into uniform electric field, $E$, from its fractional differential equation. We show that the velocity and the current density of the electrons not only depend on the time $t$, but also on the order of the fractional differential equation $\gamma$, the Drude model is a particular case. This fact could have interesting consequences in the study of electrical properties of metals.