EM wave propagation within plasma-filled rectangular waveguide using fractional space and LFD

This paper aims to investigate the propagation of the electromagnetic (EM) within the rectangular waveguide that is filled with plasma. A rapid Cherenkov free electron laser ( C-FEL) beam was injected into the plasma to excite its natural oscillations and, therefore, an EM wave was generated. We focused on TM-mode propagation through this waveguide. Exact solutions of the EM wave equation have been found using both the Laplacian operator in the fractional D-dimensional space and the local fractional derivative (LFD). The fractional solutions have been converted into classical results to simulate the usual behavior of the waves. It has been found that the well-known Bessel, Neumann, and Mittage–Leffler functions are observed and their propagation is directly proportional to fractional parameters.