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Fractional integro-differential equations for electromagnetic waves in dielectric media

V. E. Tarasov

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

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).

Keywords: fractional integro-differentiation, fractional damping, universal response, electromagnetic field, dielectric medium.

Received: 18.12.2007
Revised: 24.06.2008

DOI: 10.4213/tmf6324

 English version: Theoretical and Mathematical Physics, 2009, 158:3, 355–359

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