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

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 , 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.

Keywords:

• Fractional wave equation
• Caputo-Fabrizio operator
• fractional space-time components
• dissipative dynamics

Notes

No potential conflict of interest was reported by the authors.