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.
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