The present article is devoting a numerical approach for solving a fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM). The truncated Bernoulli and Hermite wavelets series with unknown coefficients have been used to approximate the solution in both the temporal and spatial variables. The basic idea for discretizing the FPDE is wavelet approximation based on the Bernoulli and Hermite wavelets operational matrices of integration and differentiation. The resulted system of a linear algebraic equation has been solved by the collocation method. Moreover, convergence and error analysis have been discussed. Finally, several numerical experiments with different fractional-order derivatives have been provided and compared with the exact analytical solutions to illustrate the accuracy and efficiency of the method.

翻译：本文专门用数字方法解决电介质电磁波产生的部分偏差方程(PFDE),用时间和空间变数的近似解决办法,采用了计数法,分别使用Bernoulli和Hermite波子波子序列和未知系数。FPDE的基本想法是以Bernoulli和Hermite波子波子集成和分化操作矩阵为基础的波形近似值。结果的线性代数方程系统已通过合用法解决。此外,还讨论了趋同和误差分析。最后,提供了若干使用不同分序衍生物的数值实验,并与精确的分析解决办法进行了比较,以说明方法的准确性和效率。