This work presents a boundary element method formulation for the solution of the anomalous diffusion problem. By keeping the fractional time derivative as it appears in the governing differential equation of the problem, and by employing a Weighted Residuals Method approach with the steady state fundamental solution for anisotropic media playing the role of the weighting function, one obtains the boundary integral equation of the proposed formulation. The presence of a domain integral with the fractional time derivative as part of its integrand, and the evaluation of this fractional time derivative as a Caputo derivative, constitute the main feature of the formulation. The analyses of some examples, in which the numerical results are always compared with the corresponding analytical solutions, show the robustness of the formulation, as accurate results are obtained even for small values of the order of the time derivative.

这项工作提出了解决异常扩散问题的边界元方法公式。通过保持分数微分时间导数在问题的主导微分方程中的存在，并通过对各向异性介质使用稳态基本解的加权残差法方法，来发挥加权函数的作用，可以得到方程的边界积分方程。建议的公式。分数分数导数作为其被积的一部分的域积分的存在以及对该分数分数导数作为Caputo衍生物的求值构成了制剂的主要特征。始终将数值结果与相应的分析解决方案进行比较的一些示例分析表明，该公式的鲁棒性，