We present a new numerical method for solving a wide class of time fractional partial differential equations with a space operator of general form. The proposed method is based on the Fourier series expansion along the spatial coordinate which transforms the original time fractional partial differential equations into a sequence of multi-term fractional ordinary differential equations. The fractional ordinary differential equations are solved by the use of an efficient numerical technique. The numerical examples confirm the high accuracy and efficiency of the proposed numerical scheme.

中文翻译：

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求解一类变系数时间分数阶偏微分方程的新半解析方法

我们提出了一种新的数值方法，可以用一般形式的空间算符来求解一类广泛的时间分数阶偏微分方程。所提出的方法基于沿着空间坐标的傅立叶级数展开，该展开将原始时间分数阶偏微分方程转换为一系列的多项分数阶常微分方程。分数阶常微分方程是通过使用有效的数值技术来求解的。数值算例证实了所提出数值方案的高精度和高效率。