Geodesic
Mathematical modelling of media with time dispersion using fractional derivatives
Matematičeskoe modelirovanie, Tome 25 (2013) no. 12, pp. 50-64

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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.
Mots-clés : fractal electromagnetism, fractional calculus, time dispersion.
Keywords: fractional dimention of medium 
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     author = {A. N. Bogolyubov and A. A. Koblikov and D. D. Smirnova and N. E. Shapkina},
     title = {Mathematical modelling of media with time dispersion using fractional derivatives},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {50--64},
     publisher = {mathdoc},
     volume = {25},
     number = {12},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2013_25_12_a4/}
}
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A. N. Bogolyubov; A. A. Koblikov; D. D. Smirnova; N. E. Shapkina. Mathematical modelling of media with time dispersion using fractional derivatives. Matematičeskoe modelirovanie, Tome 25 (2013) no. 12, pp. 50-64. http://geodesic.mathdoc.fr/item/MM_2013_25_12_a4/