A Boundary Element Method formulation is developed for the solution of the two-dimensional diffusion-wave problem, which is governed by a partial differential equation presenting a time fractional derivative of order α, with 1.0 < α < 2.0. In the proposed formulation, the fractional derivative is transferred to the Laplacian through the Riemann–Liouville integro-differential operator; then, the basic integral equation of the method is obtained through the Weighted Residual Method, with the fundamental solution of the Laplace equation as the weighting function. In the final expression, the presence of additional terms containing the history contribution of the boundary variables constitutes the main difference between the proposed formulation and the standard one. The proposed formulation, however, works well for 1.5 ≤ α < 2.0, producing results with good agreement with the analytical solutions and with the Finite Difference ones.

为解决二维扩散波问题开发了边界元方法公式，该公式由偏微分方程控制，该偏微分方程表示时间阶数导数为α，且1.0 <  α <2.0。在提出的公式中，分数导数通过Riemann-Liouville积分微分算子转移到Laplacian。然后，通过加权残差法，以拉普拉斯方程的基本解为加权函数，得到该方法的基本积分方程。在最后一个表达式中，包含边界变量的历史贡献的其他术语的存在构成了所提出的公式与标准公式之间的主要区别。建议的提法，但是，非常适用于1.5≤  α  <2.0，产生与分析解决方案，并与有限差分吻合较好的效果。