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 Grönwall inequality is established. Thanks to the inequality, the error estimate of a fully discrete scheme is obtained. Several numerical examples are provided to verify the effectiveness of the fully discrete numerical method.

中文翻译：

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非线性时滞分数阶抛物问题的分数阶Crank-Nicolson-Galerkin有限元方法

为了解决非线性时滞抛物线问题，提出了一种线性化数值格式。该方案基于空间方向上的标准Galerkin有限元方法，分数Crank-Nicolson方法和时间方向上的外推方法。建立了一个新颖的离散分数Grönwall不等式。由于不等式，可以获得完全离散方案的误差估计。提供了几个数值示例，以验证完全离散数值方法的有效性。