Fractional electromagnetic waves in conducting media

J.F. Gómez-Aguilar, H. Yépez-Martínez, C. Calderón-Ramón, M. Benavidez-Cruz and L.J. Morales-Mendoza

Journal of Electromagnetic Waves and Applications, 2016, vol. 30, issue 2, 259-271

Abstract: We present the fractional wave equation in a conducting material. We used a Maxwell’s equations with the assumptions that the charge density ρ$ \rho $ and current density J were zero, and that the permeability μ$ \mu $ and permittivity ϵ$ \epsilon $ were constants. The fractional wave equation will be examined separately; with fractional spatial derivative and fractional temporal derivative, finally, consider a Dirichlet conditions, the Fourier method was used to find the full solution of the fractional equation in analytic way. Two auxiliary parameters σx$ \sigma _x $ and σt$ \sigma _t $ are introduced; these parameters characterize consistently the existence of the fractional space-time derivatives into the fractional wave equation. A physical relation between these parameters is reported. The fractional derivative of Caputo type is considered and the corresponding solutions are given in terms of the Mittag-Leffler function show fractal space-time geometry different from the classical integer-order model.

Date: 2016
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DOI: 10.1080/09205071.2015.1105761

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