Geodesic
Fractional integro-differential equations for electromagnetic waves in dielectric media
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 3, pp. 419-424 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] P. Debye, Physik. Zs., 13 (1912), 97–100 | Zbl

[2] A. K. Jonscher, Universal Relaxation Law, Chelsea Dielectrics Press, London, 1996

[3] A. K. Jonscher, J. Physics D, 32:14 (1999), R57–R70 | DOI

[4] T. V. Ramakrishnan, M. R. Lakshmi (eds.), Non-Debye Relaxation in Condensed Matter, World Scientific, Singapore, 1987

[5] A. K. Jonscher, Nature, 267:5613 (1977), 673–679 ; Philos. Magazine B, 38:6 (1978), 587–601 | DOI | DOI

[6] S. G. Samko, A. A. Kilbas, O. I. Marychev, Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987 | MR | MR | Zbl

[7] G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics, Oxford Univ. Press, Oxsford, 2005 | MR | Zbl

[8] A. Carpinteri, F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics, CISM Courses and Lectures, 378, Springer, Wien, 1997 | MR | Zbl

[9] R. Hilfer (ed.), Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000 | MR | Zbl

[10] R. R. Nigmatullin, Ya. E. Ryabov, FTT, 39:1 (1997), 101–105 | DOI

[11] V. V. Novikov, V. P. Privalko, Phys. Rev. E, 64:3 (2001), 031504 | DOI

[12] Y. Yilmaz, A. Gelir, F. Salehli, R. R. Nigmatullin, A. A. Arbuzov, J. Chem. Phys., 125:23 (2006), 234705 | DOI

[13] R. R. Nigmatullin, A. A. Arbuzov, F. Salehli, A. Giz, I. Bayrak, H. Catalgil-Giz, Physica B, 388:1–2 (2007), 418–434 | DOI

[14] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Application of Fractional Differential Equations, North-Holland Math. Stud., 204, Elsevier, Amsterdam, 2006 | MR | Zbl

[15] V. E. Tarasov, G. M. Zaslavsky, Physica A, 368:2 (2006), 399–415 | DOI

[16] P. P. Nigmatullin, TMF, 90:3 (1992), 354–368 | DOI | MR | Zbl

[17] A. A. Stanislavskii, TMF, 138:3 (2004), 491–507 | DOI | MR