A physical sense for fractional modeling: The Case of damping electromagnetic waves

Electromagnetic waves are present in our daily lives, being useful in several areas. These can be seen permeating the theories of medicine, geophysics, geology, physics, among others. In geophysics, for example, they appear very frequently in electromagnetic methods, where magnetic fields, electric potentials and electromagnetic waves are used. Electromagnetic waves arise from Maxwell’s equations, which are linear equations in a vacuum or inside atoms and nuclei and, considering these cases, give rise to differential linear equations. However, the deduced equations are always solved using classical methods of solving whole order differential equations. Therefore, the objective of this work is to analyze the propagation of an electromagnetic wave in a vacuum, for an integer and fractional order equation, solving them through the modified method of Laplace decomposition (MMDL). The new proposed solution allows a variation of the fractional parameter value, rescuing the solutions of the equations of the electromagnetic waves that propagate in material media, making it possible to analyze the different types of damping for the most varied media.

Keywords
Flat electromagnetic waves; geophysics; modified method of decomposition by Laplace; fractional differential equations