Fractional Equations of Curie-von Schweidler and Gauss Laws

TL;DR

This paper derives fractional differential equations representing universal dielectric responses, specifically the Curie-von Schweidler and Gauss laws, showing that electromagnetic fields in such materials exhibit fractional damping.

Contribution

It introduces a universal fractional differential equation framework for dielectric laws, applicable across diverse materials and structures.

Findings

Derivation of fractional differential equations for dielectric response

Demonstration of fractional damping in electromagnetic fields

Universal applicability to various dielectric materials

Abstract

The dielectric susceptibility of most materials follows a fractional power-law frequency dependence that is called the "universal" response. We prove that in the time domain this dependence gives differential equations with derivatives and integrals of noninteger order. We obtain equations that describe "universal" Curie-von Schweidler and Gauss laws for such dielectric materials. These laws are presented by fractional differential equations such that the electromagnetic fields in the materials demonstrate "universal" fractional damping. The suggested fractional equations are common (universal) to a wide class of materials, regardless of the type of physical structure, chemical composition or of the nature of the polarization.