In this article we propose a scheme for solving the coupled time-fractional nonlocal diffusion problem. The scheme consist of fractional Crank-Nicolson method with Galerkin finite element method (FEM) and Newton's method. We derive \emph{a priori} error estimates for fully-discrete solutions in $L^2$ and $H^1_0$ norms. Results based on the usual finite element method are provided to confirm the theoretical estimates.

翻译：本文提出了一种求解耦合时间分数阶非局部扩散问题的方案。该方案结合了分数阶Crank-Nicolson方法、Galerkin有限元方法（FEM）以及牛顿法。我们推导了全离散解在$L^2$和$H^1_0$范数下的先验误差估计。基于常规有限元方法的结果验证了理论估计的正确性。