The generalized Cattaneo model describes the heat conduction system in the perspective of time-nonlocality. This paper proposes an accurate and robust meshless technique for approximating the solution of the time fractional Cattaneo model applied to the heat flow in a porous medium. The fractional derivative is formulated in the Caputo sense with order $1<\alpha <2$. First, a finite difference technique of convergence order $\mathcal{O}\left(\delta t^{3-\alpha }\right)$ is adopted to achieve the temporal discretization. The unconditional stability of the method and its convergence are analysed using the discrete energy technique. Then, a local meshless method based on the radial basis function partition of unity collocation is employed to obtain a full discrete algorithm. The matrices produced using this localized scheme are sparse and, therefore, they are not subject to ill-conditioning and do not pose a large computational burden. Two examples illustrate in computational terms of the accuracy and effectiveness of the proposed method.

广义 Cattaneo 模型从时间-非局域性的角度描述了热传导系统。本文提出了一种精确且稳健的无网格技术，用于逼近应用于多孔介质中热流的时间分数 Cattaneo 模型的解。分数阶导数是在 Caputo 意义上用阶表示的$1<\alpha <2$. 一、收敛阶次的有限差分法$\mathcal{哦}\left(\delta {吨}^{3-\alpha }\right)$用于实现时间离散化。使用离散能量技术分析了该方法的无条件稳定性及其收敛性。然后，采用基于统一搭配径向基函数划分的局部无网格方法得到全离散算法。使用这种局部方案生成的矩阵是稀疏的，因此，它们不会受到病态的影响，也不会造成很大的计算负担。两个例子在计算方面说明了所提出方法的准确性和有效性。