A semi-analytic numerical method is described as an efficient meshless approach for the solution of anomalous non-linear thermal conduction problems in functionally graded materials in which the model results in fractional boundary value problems. The first key feature in this scheme is the derivation and discretization of the fractional derivative at every time step. The second key feature is the trigonometric basis functions (TBFs) as the basis functions were introduced by the need for approximate solutions on boundary conditions with more flexibility in choosing collocation points. Moreover, the approximate solution of the anomalous thermal conduction problems converges to the exact solution as γ is closed to 1 in the full closed time interval for three simulated numerical results.

中文翻译：

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一种半解析搭配技术，用于求解与 Caputo 分数阶导数相关的 3D 异常非线性热传导问题


半解析数值方法被描述为一种高效的无网格方法，用于求解功能梯度材料中的异常非线性热传导问题，其中模型会导致分数边界值问题。该方案的第一个关键特征是每个时间步长的分数阶导数的推导和离散化。第二个关键特征是三角基函数 （TBF），因为基函数是由于需要边界条件的近似解而引入的，并且在选择配置点时具有更大的灵活性。此外，在三个仿真数值结果的完全闭合时间间隔内，γ接近 1，因此异常热传导问题的近似解收敛到精确解。