In this article, an efficient local meshless technique is implemented for the numerical solution of an anomalous mobile-immobile solute transport process. The process is mathematically modeled as a time fractional mobile-immobile diffusion equation in sense of Caputo derivative. An implicit time integration procedure is used to semi-discretize the model in the time direction whereas the space derivatives of the model is discretized by the proposed meshless technique based on inverse multquadric radial basis function. The demand of meshless techniques increment because of its meshless nature and simplicity of usage in higher dimensions. This technique approximate the solution on set of uniform and scattered nodes and it leads to a sparse and well-conditioned coefficient matrices. Numerical examinations on some test problems are performed to exhibit successful applications and accuracy of the local meshless technique on regular and irregular computational domains.

在本文中，一种有效的局部无网格技术被用于异常移动-不移动溶质传输过程的数值解。在Caputo导数的意义上，该过程在数学上被建模为时间分数阶的移动-固定扩散方程。使用隐式时间积分程序在时间方向上对模型进行半离散化，而该模型的空间导数则通过所提出的基于逆多径向基函数的无网格技术离散化。无网格技术的需求因其无网格性质和在更高维度上的使用简单性而增加。该技术对均匀且分散的节点集的解进行近似，从而导致稀疏且条件良好的系数矩阵。