In this paper, a meshless method with ridge basis functions for solving the time fractional two-flow domain model problem is proposed. The method uses the L1 approximation formula based on piecewise linear interpolation to discretize the Caputo time fractional derivative \( (0 < \alpha < 1) \), and by means of the ridge basis function to construct the approximation function, and uses the collocation method to discretize the governing equation. The existence and uniqueness of the numerical solution are analyzed. The error between the proposed method and the finite difference method is compared by numerical examples; then the affecting factors of the calculation accuracy are discussed. The results show that the proposed method is feasible and simple.

提出了一种具有脊基函数的无网格方法来求解时间分数两流域模型问题。该方法使用基于分段线性插值的L 1逼近公式来离散Caputo时间分数导数\（（0 <\ alpha <1）\），并通过ridge基函数来构造逼近函数，并使用搭配方法离散化控制方程。分析了数值解的存在性和唯一性。通过数值算例比较了所提方法与有限差分法之间的误差。然后讨论了影响计算精度的因素。结果表明，该方法是可行且简单的。