In this paper we apply the boundary elements method (BEM) and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of two-dimensional time-fractional partial differential equations (TFPDEs). The fractional derivative of problem is described in the Caputo sense. In BEM, the main equation deduces to solving the Helmholtz equation in each time step. Therefore, we should compute the domain integral in each time step. So, we presented an approach to compute the domain integral with no singularity. On the other hand the DRBEM has the flexibility of discretizing only the boundary of the computational domain and evaluates the solution at any required interior point. We employ the radial basis functions (RBFs) for interpolation of the inhomogeneous and time derivative terms. The proposed method is employed for solving some problems in two--dimensions on unit square and some other complex regions to demonstrate the efficiency of the proposed method.

翻译：本文应用边界元法（BEM）和双重互易边界元法（DRBEM）对二维时间分数阶偏微分方程（TFPDEs）进行数值求解。问题的分数阶导数采用Caputo意义下的定义。在BEM中，控制方程退化为在每个时间步求解亥姆霍兹方程。因此，我们需要在每个时间步计算域积分。为此，我们提出了一种无奇异性的域积分计算方法。另一方面，DRBEM具有只对计算域边界进行离散的灵活性，并能在任意所需内部点处评估解。我们采用径向基函数（RBFs）对非齐次项和时间导数项进行插值。所提出的方法被应用于单位正方形及其他复杂区域上的若干二维问题求解，以验证该方法的有效性。