Electromagnetic field in a conducting medium modeled by the fractional Ohm’s law

Abstract

Classical telegrapher’s equations for electromagnetic field in a conducting medium, which are the consequence of coupling Maxwell’s equations, charge conservation law and Ohm’s law, are generalized by modeling medium’s conducting properties using two types of fractional Ohm’s laws, that include terms accounting for instantaneous and hereditary contribution of electric field to current density, with the hereditary term expressed either through the fractional integral or derivative. Solving the initial value problem for the above mentioned system of equations, the electromagnetic field vectors are obtained in terms of convolution of Green’s function with the initial spatial distribution of electromagnetic field vector describing the evolution of electromagnetic field. It is shown that the propagating nature of the electromagnetic field is due to distributional nature of Green’s function.