In this article, the variable‐order (VO) time fractional 2D Kuramoto‐Sivashinsky equation is introduced, and a semidiscrete approach is presented through 2D Chebyshev cardinal functions (CCFs) for solving this equation. In the proposed method, we obtain a recurrent algorithm by using the finite difference method to approximate the VO fractional differentiation, the weighted finite difference method with parameter θ, and the approximation of the unknown function by the 2D CCFs. The differentiation operational matrices and the collocation technique are used to extract a linear system of algebraic equations which can be easily solved. The credibility of the developed method is examined on three numerical examples.

中文翻译：

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基于切比雪夫基数函数的数值方法，用于四阶二维Kuramoto-Sivashinsky方程的变阶分数形式

在本文中，介绍了二维时间可变分数（VO）时间Kuramoto-Sivashinsky方程，并通过2D Chebyshev基函数（CCF）提出了一种半离散方法来求解该方程。在所提出的方法中，我们使用有限差分法近似VO分数微分，使用参数θ的加权有限差分法以及二维CCF对未知函数的近似，从而得到递归算法。微分运算矩阵和搭配技术用于提取可以轻松求解的线性代数方程组。在三个数值示例上检验了所开发方法的可靠性。