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.

本文旨在研究电磁 (EM) 在充满等离子体的矩形波导内的传播。将快速切伦科夫自由电子激光 (C-FEL) 光束注入等离子体中以激发其自然振荡，从而产生电磁波。我们重点研究通过该波导的 TM 模式传播。使用分数 D 维空间中的拉普拉斯算子和局部分数阶导数 (LFD) 已经找到了 EM 波动方程的精确解。分数解已转换为经典结果，以模拟波浪的通常行为。人们发现，观察到著名的贝塞尔函数、诺伊曼函数和米塔奇-莱弗勒函数，它们的传播与分数参数成正比。