A linearized numerical scheme is proposed to solve the nonlinear time fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson method and extrapolation methods in the temporal direction. A novel discrete fractional Gr\"{o}nwall inequality is established. Thanks to the inequality, the error estimate of fully discrete scheme is obtained. Several numerical examples are provided to verify the effectiveness of the fully discrete numerical method.

翻译：提议一个线性数字方案, 以解决非线性时间分数抛物线问题, 并延迟时间。 这个方案基于空间方向的Galerkin定点元素标准方法、 分数 Clank- Nicolson 方法和时间方向的外推法。 建立了一个新颖的离散分数 Gr\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\Nn wall 不平等性。 由于不平等性, 获得了完全离散的图案的错误估计。 提供了多个数字示例, 以验证完全离散的数字方法的有效性 。