Fractional Power-Law Spatial Dispersion in Electrodynamics

TL;DR

This paper explores fractional calculus models to describe electric fields in non-local media with power-law spatial dispersion, generalizing classical laws like Coulomb's law and Debye screening.

Contribution

It introduces fractional differential equations involving the fractional Laplacian to model non-local media with power-law dispersion, extending classical electrodynamics theories.

Findings

Generalized Coulomb's law for power-law media

Fractional models describe anomalous plasma behavior

Characterized Debye screening in non-local media

Abstract

Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb's law and Debye's screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type.