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

Author

Listed:
  • J. F. Gomez-Aguilar
  • R. F. Escobar-Jimenez
  • M. G. Lopez-Lopez
  • V. M. Alvarado-Martinez
  • T. Cordova-Fraga

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.

Suggested Citation

  • J. F. Gomez-Aguilar & R. F. Escobar-Jimenez & M. G. Lopez-Lopez & V. M. Alvarado-Martinez & T. Cordova-Fraga, 2016. "Electromagnetic waves in conducting media described by a fractional derivative with non-singular kernel," Journal of Electromagnetic Waves and Applications, Taylor & Francis Journals, vol. 30(11), pages 1493-1503, July.
    • Handle: RePEc:taf:tewaxx:v:30:y:2016:i:11:p:1493-1503
    DOI: 10.1080/09205071.2016.1204252
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