This paper develops an efficient local meshless collocation algorithm for approximating the time fractional evolution model that is applied for the modeling of heat flow in materials with memory. The model is based on the Riemann-Liouville fractional integral. The proposed method discretizes the unknown solution using two main parts. First, the temporal direction is approximated through the second-order finite difference scheme. Second, the spatial direction of the governing problem is discretized via the local radial basis function partition of unity technique. The major drawback of global collocation techniques is the computational cost associated with arisen dense algebraic system. This localized method is based on partitioning the original domain to several subdomains by means of the kernel approximation on each local domain and allows one to significantly sparsify the algebraic system having small condition number in addition to lowering the computational cost. The stability and convergence of the time difference formulation are discussed in detail with respect to the $H^1$-norm. Numerical results and comparisons are illustrated in order to confirm theoretical analysis and the accuracy of the method.

本文开发了一种有效的局部无网格搭配算法，用于逼近时间分数演化模型，该模型应用于具有记忆的材料中的热流建模。该模型基于 Riemann-Liouville 分数积分。所提出的方法使用两个主要部分对未知解进行离散化。首先，时间方向通过二阶有限差分格式近似。其次，控制问题的空间方向通过统一技术的局部径向基函数划分进行离散化。全局搭配技术的主要缺点是与出现的密集代数系统相关的计算成本。这种局部化方法基于通过每个局部域上的核近似将原始域划分为几个子域，并且除了降低计算成本外，还允许显着稀疏具有小条件数的代数系统。时差公式的稳定性和收敛性在以下方面进行了详细讨论$H^1$-规范。说明了数值结果和比较，以确认理论分析和方法的准确性。