Abstract Multi-term time-fractional partial differential equations (PDEs) have become a hot topic in the field of mathematical physics and are used to improve the modeling accuracy in the description of anomalous diffusion processes compared to the single-term PDE results. This research includes the numerical solutions of two-term time-fractional PDE models using an efficient and accurate local meshless method. Due to the advantages of the meshless nature and ease of applicability in higher dimensions, the demand for meshless techniques is increasing. This approach approximates the solution on a uniform or scattered set of nodes, resulting in well-conditioned and sparse coefficient matrices. Numerical tests are performed to demonstrate the efficacy and accuracy of the proposed local meshless technique.

中文翻译：

---

使用局部无网格方法求解数学物理中出现的两项时间分数 PDE 模型的数值解

摘要 多项时间分数偏微分方程(PDE)已成为数学物理领域的一个热门话题，与单项PDE结果相比，它被用于提高异常扩散过程描述的建模精度。这项研究包括使用有效和准确的局部无网格方法的两项时间分数 PDE 模型的数值解。由于无网格特性和在更高维度上易于应用的优点，对无网格技术的需求正在增加。这种方法在统一或分散的节点集上逼近解，从而产生条件良好且稀疏的系数矩阵。进行数值测试以证明所提出的局部无网格技术的有效性和准确性。