This paper aims to provide a new numerical method for solving variable‐order fractional diffusion equations. The method is constructed using fractional‐order Taylor wavelets. By using the regularized beta function, a formula for computing the exact value of Riemann‐Liouville fractional integral operator of the fractional‐order Taylor wavelets is given. The Taylor wavelets properties and the formula are used in combination with a spectral collocation method to reduce the given diffusion equation to a system of algebraic equations. The method is easy to implement, and gives very accurate solutions. Several examples are given to show the applicability and the effectiveness of the method.

中文翻译：

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使用分数阶泰勒小波求解变量阶分数阶扩散方程的数值方法

本文旨在为求解变分分数阶扩散方程提供一种新的数值方法。该方法是使用分数阶泰勒小波构造的。通过使用正则化的beta函数，给出了用于计算分数阶泰勒小波的Riemann-Liouville分数积分算子的精确值的公式。泰勒小波性质和公式与频谱搭配方法结合使用，可以将给定的扩散方程式简化为代数方程式系统。该方法易于实施，并且给出了非常准确的解决方案。给出了几个例子来说明该方法的适用性和有效性。