This paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy discrete counterparts of these conditions have conservation laws that approximate the continuous ones. On the basis of this result, we derive conservation laws for a mixed scheme that combines a finite difference method in space with a spectral integrator in time. A range of numerical experiments shows the convergence of the proposed method and its conservation properties.

中文翻译：

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时间分数扩散偏微分方程的数值守恒定律

本文介绍了确定任意分数阶扩散方程的守恒定律的充分条件。满足这些条件的离散对应物的数值方法具有近似于连续条件的守恒定律。在此结果的基础上，我们推导了混合方案的守恒定律，该方案将空间中的有限差分方法与时间上的谱积分器相结合。一系列数值实验表明了所提出方法的收敛性及其守恒特性。