Caputo 分数阶导数的正弦与余弦扩散表示
The sine and cosine diffusive representations for the Caputo fractional derivative
AI总结：
针对 Caputo 分数阶导数非局部性导致数值方法耗时且耗内存的问题，本文提出了两种新的扩散表示方法用于近似阶数为 $0<α<1$ 的 Caputo 分数阶导数，并给出了误差分析与数值算例。
摘要：
如我们所知，已有多种方法被提出用于数值近似 Caputo 分数阶导数。这些方法的一个共同挑战是 Caputo 分数阶导数的非局部性质，这导致方法运行缓慢且消耗内存。分数阶导数的扩散表示是克服上述挑战的有效工具。本文提出了两种新的扩散表示，用于近似阶数为 $0<α<1$ 的 Caputo 分数阶导数。文末给出了新方法的误差分析及一些数值算例。
英文摘要：
As we are aware, various types of methods have been proposed to approximate the Caputo fractional derivative numerically. A common challenge of the methods is the non-local property of the Caputo fractional derivative which leads to the slow and memory consuming methods. Diffusive representation of fractional derivative is an efficient tool to overcome the mentioned challenge. This paper presents two new diffusive representations to approximate the Caputo fractional derivative of order $0<α<1$. Error analysis of the newly presented methods together with some numerical examples are provided at the end.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
