A time-fractional diffusion equation involving the Dirichlet energy is considered with nonlocal diffusion operator in the space which has dimension $d\in \{2,3\}$ and the Caputo sense fractional derivative in time. Further, nonlocal term in diffusion operator is of Kirchhoff type. We discretize the space using the Galerkin finite elements and time using the finite difference scheme on a uniform mesh. First, we prove the existence and uniqueness of a fully discrete numerical solution of the problem using the Brouwer fixed point theorem. Then, we give a priori bounds and convergence estimates in $L^2$ and $L^{\infty }$ norms for fully-discrete problem. A more delicate analysis in the error provides the second order convergence for the proposed scheme. Numerical results are provided to validate the theoretical analysis.

在具有维数的空间中使用非局部扩散算子考虑了涉及狄利克雷能量的时间分数阶扩散方程 $d\in \{2，3\}$Caputo可以及时感知分数导数。此外，扩散算子中的非局部项是Kirchhoff类型的。我们使用Galerkin有限元离散空间，并使用有限差分方案在均匀网格上离散时间。首先，我们使用Brouwer不动点定理证明问题的完全离散数值解的存在性和唯一性。然后，我们给出一个先验边界和收敛估计${\mathrm{大号}}^2$ 和 ${\mathrm{大号}}^{\infty }$完全离散问题的规范。误差的更精细分析为所提出的方案提供了二阶收敛性。提供数值结果以验证理论分析。