Fractional electromagnetic waves in conducting media.

We present the fractional wave equation in a conducting material. We used a Maxwell’s equations with the assumptions that the charge densityand current densityJwere zero, and that the permeabilityand permittivitywere 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 parametersandare 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. [ABSTRACT FROM AUTHOR]