In this work, we solve distributed order diffusion equations (DODEs) by applying the theory on reproducing kernel functions (RKFs). The classical numerical quadrature formulae is used to approximate the DODE to a multi‐term Caputo fractional order diffusion equation (FDE). The Mittag‐Leffler RKF is introduced to estimate fractional derivatives of Caputo. And a space–time RKFs collocation scheme is derived for the multi‐term Caputo time FDEs. The accuracy of the present numerical technique is indicated by employing several experiments.

中文翻译：

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分布函数扩散方程的基于核函数的方法

在这项工作中，我们通过将理论应用到再生核函数（RKF）上来解决分布式阶扩散方程（DODE）。经典的数值正交公式用于将DODE近似为多项Caputo分数阶扩散方程（FDE）。引入了Mittag-Leffler RKF来估计Caputo的分数导数。并针对多时元Caputo时间FDE导出了时空RKF配置方案。通过采用几个实验表明了本数值技术的准确性。