In this article, a numerical scheme is introduced for solving the fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM) by using an efficient class of finite difference methods. The numerical scheme is based on the Hermite formula. The Caputo's fractional derivatives in time are discretized by a finite difference scheme of order $\mathcal{O}(k^{(4-\alpha)})$ \& $\mathcal{O}(k^{(4-\beta)})$, $1<\beta <\alpha \leq 2$. The stability and the convergence analysis of the proposed methods are given by a procedure similar to the standard von Neumann stability analysis under mild conditions. Also for FPDE, accuracy of order $\mathcal{O}\left( k^{(4-\alpha)}+k^{(4-\beta)}+h^2\right) $ is investigated. Finally, several numerical experiments with different fractional-order derivatives are provided and compared with the exact solutions to illustrate the accuracy and efficiency of the scheme. A comparative numerical study is also done to demonstrate the efficiency of the proposed scheme.

翻译：在本篇文章中,采用了一个数字方案来解决电介质电磁波产生的部分偏差方程(PFDE),即1 ⁇ beta ⁇ alpha\leq 2$。拟议方法的稳定性和趋同分析是通过类似于标准von Neumann稳定性分析的程序在温和条件下进行的。对于FPDE, 也进行了比较性研究,还进行了比较性研究,以说明拟议办法的准确性。还进行了比较性研究,以说明拟议办法的准确性。