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.

传导介质中电磁场的经典电报方程是耦合麦克斯韦方程、电荷守恒定律和欧姆定律的结果，通过使用两种类型的分数欧姆定律对介质的传导特性进行建模来推广，其中包括考虑瞬时和遗传的术语电场对电流密度的贡献，遗传术语通过分数积分或导数表示。解决上述方程组的初始值问题，通过格林函数与描述电磁场演变的电磁场矢量的初始空间分布的卷积获得电磁场矢量。