This paper represents a system of variable‐order (VO) time fractional 2D Burgers equations and expresses a semidiscrete approach by applying the 2D Chelyshkov polynomials (CPs) for solving this system. In this model, the fractional derivative of the Caputo type is considered. To solve this system, we first discretize the VO time fractional derivatives. Next, we obtain a recurrent algorithm by using the weighted finite difference method with parameter θ. Then, utilizing the 2D CPs, we expand the unknown solution and replace it in the main system. In the sequel, we use the differentiation operational matrices and the collocation method to extract an algebraic system of equations which can be easily solved. The validity of the formulated method is investigated through three numerical examples.

中文翻译：

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二维Chelyshkov多项式耦合2D Burgers方程的变分分数版的数值方法。

本文表示了一个可变阶（VO）时间分数2D Burgers方程组，并通过应用2D Chelyshkov多项式（CP）求解该系统来表示一种半离散方法。在此模型中，考虑了Caputo类型的分数导数。为了解决这个系统，我们首先离散化VO时间分数导数。接下来，我们通过使用带有参数θ的加权有限差分法获得递归算法。然后，利用2D CP，我们扩展未知解决方案并将其替换在主系统中。在续集中，我们使用微分运算矩阵和搭配方法来提取可以轻松求解的代数方程组。通过三个数值例子研究了所提方法的有效性。