Electromagnetic waves in conducting media described by a fractional derivative with non-singular kernel

J. F. Gomez-Aguilar, R. F. Escobar-Jimenez, M. G. Lopez-Lopez, V. M. Alvarado-Martinez and T. Cordova-Fraga

Journal of Electromagnetic Waves and Applications, 2016, vol. 30, issue 11, 1493-1503

Abstract: In this paper, we present an alternative representation of the wave equation in a conducting material. We derive special solutions for the space-time derivatives using the Caputo-Fabrizio fractional operator in the range β,γ∈(0;1]$ \beta ,\gamma \in (0;1] $, respectively. Using an iterative technique that involves the Laplace transform and its inverse, we derive new coupled-solutions of the wave equation. Some numerical simulations obtained showed different behaviors when compared with classical model solutions. The corresponding solutions show fractal space-time geometry different from the classical integer-order model.

Date: 2016
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DOI: 10.1080/09205071.2016.1204252

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