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A fractional order diffusion-wave equation for time-dispersion media

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Abstract

Electromagnetic fields in time-dispersion media with a power-law dependence on time are analyzed. It is shown that these media are fractal and their fractal dimension is determined. Equations for scalar and vector potentials are derived using analogues of Maxwell’s equations for these types of media with the use of Caputo fractional derivatives. Electromagnetic fields in a bounded domain are numerically calculated for arbitrary functions of charge and current.

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References

  1. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Fractional Order Derivatives and Some Their Applications (Nauka Tekh., Minsk, 1987) [in Russian].

    MATH  Google Scholar 

  2. A. M. Nakhushev, Fractional Calculus and Its Use (Fizmatlit, Moscow, 2003) [in Russian].

    Google Scholar 

  3. E. Feder, Fractals (Plenum, New York, 1988; Mir, Moscow, 1991) [in Russian].

    MATH  Google Scholar 

  4. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics (Nauka, Moscow, 1972) [in Russian].

    Google Scholar 

  5. V. F. Kravchenko and V. L. Rvachev, Algebra of Logic, Atomic Functions and Wavelets in Physical Applications (Fizmatlit, Moscow, 2006) [in Russian].

    Google Scholar 

  6. A. N. Bondarenko and D. S. Ivashchenko, Sib. Elektron. Mat. Izv. 5, 581 (2008).

    MathSciNet  Google Scholar 

  7. A. A. Potapov, Fractals in Radiophysics and Radiolocation: Topology of Choice (Univ. Kniga, Moscow, 2005) [in Russian].

    Google Scholar 

  8. A. N. Bogolyubov, A. A. Potapov, and S. Sh. Rekhviashvili, Moscow Univ. Phys. Bull. 64, 365 (2009).

    Article  ADS  MATH  Google Scholar 

  9. B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, New York, 1982).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Physics, Moscow State University, Moscow, 11999, Russia

    A. N. Bogolyubov, A. A. Koblikov, D. D. Smirnova & N. E. Shapkina

Authors
  1. A. N. Bogolyubov
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  2. A. A. Koblikov
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  3. D. D. Smirnova
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  4. N. E. Shapkina
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Additional information

Original Russian Text © A.N. Bogolyubov, A.A. Koblikov, D.D. Smirnova, N.E. Shapkina, 2012, published in Vestnik Moskovskogo Universiteta. Fizika, 2012, No. 5, pp. 13–17.

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Bogolyubov, A.N., Koblikov, A.A., Smirnova, D.D. et al. A fractional order diffusion-wave equation for time-dispersion media. Moscow Univ. Phys. 67, 423–428 (2012). https://doi.org/10.3103/S0027134912050037

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  • DOI: https://doi.org/10.3103/S0027134912050037

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