The time-fractional problem is a class of important models to represent the real world. It is an open problem to study how the fractional operator acts on the surface. In this work, we present and analyze a meshless local radial point collocation method for numerically solving time-fractional convection-diffusion equations on closed surfaces embedded in ℝ3. The second-order shifted Grünwald scheme is applied in time discretization. All computations use only extrinsic coordinates to avoid coordinate distortions and singularities. Moreover, the stability and convergence of the method are proven by the energy estimate. Numerical experiments are provided to support the convergence analysis and numerical performance of the proposed method.

中文翻译：

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一种模拟表面上时间-分数对流-扩散方程的无网格局部径向点配置方法

时间分数问题是代表现实世界的一类重要模型。研究分数算子如何作用于曲面是一个悬而未决的问题。在这项工作中，我们提出并分析了一种无网格的局部径向点配置方法，用于数值求解嵌入在封闭表面上的时间分数对流扩散方程ℝ3. 二阶移位的 Grünwald 格式应用于时间离散化。所有计算仅使用外部坐标以避免坐标失真和奇异性。此外，能量估计证明了该方法的稳定性和收敛性。提供了数值实验来支持所提出方法的收敛性分析和数值性能。