This paper considers a novel numerical method based on Lucas‐fractional Lucas functions (L‐FL‐Fs) and collocation method for solving the distributed‐order time‐fractional diffusion equations. In the current investigation, we express the new computational process to gain the integral operational matrix for Lucas polynomials (LPs) and fractional Lucas functions (FLFs). The proposed method creates operational matrices with high accuracy that affect to accuracy and efficiency of the computational scheme directly. The operational matrices, by combining Legendre–Gauss quadrature rule and collocation method, reduce the given distributed‐order time‐fractional diffusion equation to a system of algebraic equations. Also, we investigate the error estimation associated with the presented idea. At last, several examples are given to demonstrate the accuracy and easy implementation of the proposed method.

中文翻译：

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改进的离散时间分数维扩散方程数值技术

本文考虑了一种基于Lucas-分数阶Lucas函数（L-FL-Fs）和搭配方法的新型数值方法，用于求解分布时间分数阶扩散方程。在当前的研究中，我们表达了一种新的计算过程来获得卢卡斯多项式（LPs）和分数卢卡斯函数（FLF）的积分运算矩阵。所提出的方法创建具有高精度的运算矩阵，其直接影响计算方案的精度和效率。运算矩阵通过结合勒让德－高斯正交规则和并置方法，将给定的分布时间分数阶扩散方程简化为代数方程组。此外，我们调查与提出的想法相关的错误估计。终于，