In this paper, the Chebyshev–Gauss–Lobatto collocation method is developed for studying the variable-order (VO) time fractional model of the generalized Hirota–Satsuma coupled KdV system arising in interaction of long waves. To define this new system, the Atangana–Baleanu fractional operator is implemented. The operational matrix of VO fractional differentiation for the shifted Chebyshev polynomials is extracted and then, a collocation scheme is established to reduce the original VO fractional problem to a system of nonlinear algebraic equations. The validity of the presented method is investigated on two numerical examples.

中文翻译：

---

变阶时间分数阶广义Hirota-Satsuma耦合KdV系统的Chebyshev-Gauss-Lobatto配置方法

在本文中，开发了 Chebyshev-Gauss-Lobatto 搭配方法，用于研究长波相互作用中产生的广义 Hirota-Satsuma 耦合 KdV 系统的变阶 (VO) 时间分数模型。为了定义这个新系统，实现了 Atangana-Baleanu 分数运算符。提取了移位切比雪夫多项式的VO分数微分运算矩阵，然后建立了搭配方案，将原始VO分数问题化简为非线性代数方程组。在两个数值例子上研究了所提出方法的有效性。