A. N. Bogolyubov, A. A. Koblikov, D. D. Smirnova, N. E. Shapkina, “Mathematical modelling of media with time dispersion using fractional derivatives”, Mat. Model., 25:12 (2013), 50

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Matematicheskoe modelirovanie, 2013, Volume 25, Number 12, Pages 50–64 (Mi mm3429)

This article is cited in 4 scientific papers (total in 4 papers)

Mathematical modelling of media with time dispersion using fractional derivatives

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

Lomonosov Moscow State University, Chair of Mathematics, Faculty of Рhysics

Full-text PDF (559 kB) Citations (4)

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Abstract: Electromagnetic fields in time-dispersed media with power dependence are analysed. It is shown that these media have fractal properties. Their fractal dimension is determined. The equations for scalar and vector potentials are found using Maxwell’s equations analogues presented with the help of Caputo differintegral. Electromagnetic fields are numerically calculated in bounded domain for arbitrary functions of charge and current.

Keywords: fractal electromagnetism, fractional dimention of medium, fractional calculus, time dispersion.

Received: 18.06.2012

Bibliographic databases:

Document Type: Article

UDC: 530.1+537

Language: Russian

Citation: A. N. Bogolyubov, A. A. Koblikov, D. D. Smirnova, N. E. Shapkina, “Mathematical modelling of media with time dispersion using fractional derivatives”, Mat. Model., 25:12 (2013), 50–64

Citation in format AMSBIB

\Bibitem{BogKobSmi13}

\by A.~N.~Bogolyubov, A.~A.~Koblikov, D.~D.~Smirnova, N.~E.~Shapkina

\paper Mathematical modelling of media with time dispersion using fractional derivatives

\jour Mat. Model.

\yr 2013

\vol 25

\issue 12

\pages 50--64

\mathnet{http://mi.mathnet.ru/mm3429}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3221129}

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https://www.mathnet.ru/eng/mm3429

https://www.mathnet.ru/eng/mm/v25/i12/p50

This publication is cited in the following 4 articles:

B. Yu. Irgashev, “A boundary value problem with conjugation conditions for a degenerate the equations with the Caputo fractional derivative”, Russian Math. (Iz. VUZ), 66:4 (2022), 24–31
B. Yu. Irgashev, “On a Problem with Conjugation Conditions for an Equation of Even Order Involving a Caputo Fractional Derivative”, Math. Notes, 112:2 (2022), 215–222
L. I. Moroz, A. G. Maslovskaya, “Numerical simulation of an anomalous diffusion process based on the higher-order accurate scheme”, Math. Models Comput. Simul., 13:3 (2021), 492–501
L. I. Moroz, A. G. Maslovskaya, “Hybrid stochastic fractal-based approach to modelling ferroelectrics switching kinetics in injection mode”, Math. Models Comput. Simul., 12:3 (2020), 348–356

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	497
Full-text PDF :	143
References:	77
First page:	34

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