Fractional Integro-Differential Equations for Electromagnetic Waves in Dielectric Media

TL;DR

This paper derives fractional integro-differential equations to model electromagnetic wave propagation in dielectric media exhibiting fractional power-law relaxation, providing a unified mathematical framework across various materials.

Contribution

It introduces a novel fractional calculus approach to describe electromagnetic fields in dielectrics with power-law susceptibility, unifying diverse media types under a common model.

Findings

Electromagnetic fields follow fractional power-law relaxation.

Derived equations apply broadly across dielectric media.

Model captures wide frequency range behavior.

Abstract

We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equations with time derivatives of noninteger order. We obtain fractional integro-differential equations for electromagnetic waves in a dielectric. The electromagnetic fields in dielectrics demonstrate a fractional power-law relaxation. The fractional integro-differential equations for electromagnetic waves are common to a wide class of dielectric media regardless of the type of physical structure, the chemical composition, or the nature of the polarizing species (dipoles, electrons, or ions).