This paper develops the solution of the two-dimensional time fractional evolution model using finite difference scheme derived from radial basis function (RBF-FD) method. In this discretization process, a finite difference formula is implemented to discrete the temporal variable, while the local RBF-FD formulation is utilized to approximate the spatial variable. The pattern of data distribution in the local support domain is assumed as having a fixed number of nodes. The local RBF-FD is based on the local support domain that leads to a sparsity system and also avoids the ill-conditioning problem caused by global collocation method. The stability and convergence of time-discrete approach in $H^1$-norm are discussed by means of the energy method. Numerical results illustrate the proposed method and demonstrate that it provides accurate solutions on regular and irregular computational domains.

本文采用基于径向基函数（RBF-FD）方法的有限差分方案，开发了二维时间分数演化模型的解。在该离散化过程中，使用有限差分公式来离散时间变量，而使用局部RBF-FD公式来近似空间变量。假定本地支持域中的数据分发模式具有固定数量的节点。本地RBF-FD基于本地支持域，这导致了稀疏系统，还避免了由全局配置方法引起的病态问题。离散时间方法的稳定性和收敛性$H^{\mathrm{1个}}$-范数通过能量法讨论。数值结果说明了该方法，并证明了该方法可以在规则和不规则计算域上提供准确的解决方案。