In this paper, the unstructured mesh Galerkin finite element method with a weighted and shifted Grünwald difference approximation and Composite Trapezoid formula is presented to solve the nonhomogeneous two-dimensional distributed order time fractional Cable equation on irregular convex domains. The Crank–Nicolson type discretization of the finite element scheme is implemented to obtain the numerical solution. The stability and convergence of the numerical scheme are discussed and derived. Finally, some numerical examples on irregular convex domains are given to confirm our theoretical results.

中文翻译：

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二维分布时间分数电缆方程的一种新的有限元方法

为了解决不规则凸域上的非均匀二维分布时间分数Cable方程，提出了一种具有加权移位的Grünwald差分近似和复合梯形公式的非结构网格Galerkin有限元方法。实施有限元方案的Crank–Nicolson型离散化以获得数值解。讨论并推导了数值方案的稳定性和收敛性。最后，给出了关于不规则凸域的一些数值例子，以证实我们的理论结果。