The fractional nonlinear coupled viscous Burgers and Korteweg-de Vries (KdV) evolutionary equations model various interesting phenomena in engineering and applied sciences. Therefore, their accurate numerical modeling and solution behavior are very important. In this article, radial basis functions (RBFs) approach is proposed and analyzed for the numerical solutions of time-fractional coupled Burgers’ and KdV equations. RBFs together with collocation method are employed in space approximation. A simple quadrature formula combined with finite difference of \(\mathscr {O}{(\Delta t^{2-\alpha })},\,(0<\alpha \le 1)\) is used for temporal discretization. For the proposed method, eigenvalue stability analysis is carried out theoretically and confirmed via numerical examples for RBFs shape parameter \(\beta\). The proposed method is meshfree thus reduces the computational cost of mesh generation. Various test problems are considered for the method validation. Simulated results show good agreement with exact solutions and earlier works presented in graphical and tabulated forms. Accuracy and efficiency of the proposed method are assessed using discrete \({e}_{2}\), \({e}_{\infty }\) and \({e}_{\text {rms}}\) error norms.

分数阶非线性耦合粘性Burgers和Korteweg-de Vries（KdV）演化方程可对工程和应用科学中的各种有趣现象进行建模。因此，它们的精确数值建模和求解行为非常重要。在本文中，提出了径向基函数（RBFs）方法并分析了时间分数耦合Burgers和KdV方程的数值解。RBF与搭配方法一起用于空间逼近。将简单的正交公式与\（\ mathscr {O} {（\ Delta t ^ {2- \ alpha}}}，\，（0 <\ alpha \ le 1）\）的有限差分组合起来用于时间离散化。对于所提出的方法，从理论上进行了特征值稳定性分析，并通过数值示例验证了RBFs形状参数。\（\ beta \）。所提出的方法是无网格的，因此减少了网格生成的计算成本。方法验证考虑了各种测试问题。模拟结果显示出与精确解决方案的良好一致性，并且以图形和表格形式显示了早期的工作。使用离散\（{e} _ {2} \），\（{e} _ {\ infty} \）和\（{e} _ {\ text {rms}}}来评估所提出方法的准确性和效率）错误规范。