In this paper, the boundary element method is combined with Chebyshev operational matrix technique to solve two‐dimensional multiorder time‐fractional partial differential equations: nonlinear and linear in respect to spatial and temporal variables, respectively. Fractional derivatives are estimated by Caputo sense. Boundary element method is used to convert the main problem into a system of a multiorder fractional ordinary differential equation. Then, the produced system is approximated by Chebyshev operational matrix technique, and its condition number is analyzed. Accuracy and efficiency of the proposed hybrid scheme are demonstrated by solving three different types of two‐dimensional time‐fractional convection–diffusion equations numerically. The convergent rates are calculated for different meshing within the boundary element technique. Numerical results are given by graphs and tables for solutions and different type of error norms.

中文翻译：

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用边界元法和切比雪夫矩阵求解多阶时间分数维对流扩散反应方程的新方法

本文将边界元方法与Chebyshev运算矩阵技术相结合，以求解二维多阶时间分数阶偏微分方程：分别针对空间和时间变量的非线性和线性。小数导数通过Caputo感测来估计。使用边界元方法将主要问题转换为多阶分数阶常微分方程组。然后，使用切比雪夫运算矩阵技术对生成的系统进行近似，并分析其条件数。通过数值求解三种不同类型的二维时间分数对流扩散方程，证明了所提混合方案的准确性和效率。在边界元技术中针对不同的网格计算收敛速率。