In this article, the non-singular variable-order fractional derivative in the Heydari-Hosseininia concept is used to formulate the variable-order fractional form of the coupled nonlinear Ginzburg-Landau equations. To solve this system, a numerical scheme is constructed based upon the shifted Vieta-Lucas polynomials. In this method, with the help of classical and fractional derivative matrices of the shifted Vieta-Lucas polynomials (which are extracted in this study), solving the studied problem is transformed into solving a system of nonlinear algebraic equations. The convergence analysis and the truncation error of the shifted Vieta-Lucas polynomials in two dimensions are investigated. Numerical problems are demonstrated to confirm the convergence rate of the presented algorithm.

在本文中，使用Heydari-Hosseininia概念中的非奇异分数阶分数导数来表示耦合非线性Ginzburg-Landau方程的分数阶分数形式。为了解决该系统，基于移位的Vieta-Lucas多项式构造了数值方案。在这种方法中，借助于移位的Vieta-Lucas多项式的经典和分数阶导数矩阵（在本研究中提取），将研究问题的求解转化为求解非线性代数方程组。研究了二维位移Vieta-Lucas多项式的收敛性分析和截断误差。数值问题证明了所提出算法的收敛速度。