Geodesic
Fractional integro-differential equations for electromagnetic waves in dielectric media
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 3, pp. 419-424

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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. 
@article{TMF_2009_158_3_a7,
     author = {V. E. Tarasov},
     title = {Fractional integro-differential equations for electromagnetic waves in dielectric media},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {419--424},
     publisher = {mathdoc},
     volume = {158},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a7/}
}
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V. E. Tarasov. Fractional integro-differential equations for electromagnetic waves in dielectric media. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 3, pp. 419-424. http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a7/