In this paper, we attempt to find an approximate solution of time-fractional coupled nonlinear Schrödinger equations (TFCNLS) through one of the meshless approach based on radial basis functions (RBFs) collocation. The time-fractional derivative is described in terms of the Caputo derivative. Discretizing the time-fractional derivative of the mentioned equation, we first use a scheme of order $O\left(\mathrm{\Delta }{t}^{2-\alpha }\right)$, $0<\alpha \le 1,$ and then the average value of the function in a consecutive time step is used for other terms. Also, we use the RBFs collocation method to approximate the spatial derivative. On the other hand, the stability analysis of the suggested scheme is investigated in a similar way to the classic von Neumann technique for TFCNLS equations. This present paper is to indicate that the meshfree methods are appropriate and reliable to obtain a numerical solution of fractional partial differential equations. This efficiency and accuracy of the present method are verified by solving two examples. We obtain the numerical results from solving this problem on the rectangular domain. All obtained numerical experiments are presented in tables and figures. Finally, it can be said that the main advantage of the mentioned scheme is that the algorithm is very simple and easy to apply.

在本文中，我们尝试通过一种基于径向基函数（RBF）配置的无网格方法，找到时间分数阶耦合非线性Schrödinger方程（TFCNLS）的近似解。时间分数导数是用Caputo导数描述的。离散化提到的方程式的时间分数阶导数，我们首先使用阶数方案$Ø（\mathrm{\Delta }{Ť}^{\mathrm{2个}-\alpha }）$， $0<\alpha \le \mathrm{1个}，$然后将连续时间步长中的函数平均值用于其他项。此外，我们使用RBF搭配方法来近似空间导数。另一方面，建议的方案的稳定性分析以与TFCNLS方程的经典von Neumann技术相似的方式进行研究。本文旨在指出，无网格方法对于分数阶偏微分方程的数值解是合适且可靠的。通过解决两个例子，验证了本方法的效率和准确性。通过在矩形域上解决此问题，我们获得了数值结果。所有获得的数值实验均在表和图中给出。最后，