A nonlinear initial boundary value problem with a time Caputo derivative of fractional-order $\beta \in (1,2)$ and a space Riesz derivative of fractional-order $\alpha \in (1,2)$ is considered. A linearized alternating direction implicit (ADI) scheme for this problem is constructed and analysed. First, we use the classical central difference formula and a new $3-\beta$-order formula to approximate the second-order derivative and the Caputo derivative in temporal direction, respectively. Meanwhile, the central difference quotient and fractional central difference formula are applied to deal with the spatial discretizations. Then, the proposed ADI scheme is proved unconditionally stable and convergent with the $3-\beta$-order accuracy in time and the second-order accuracy in space. Furthermore, the effectiveness of the ADI scheme and theoretical findings are illustrated by numerical experiments.

具有分数阶时间 Caputo 导数的非线性初边值问题 $\beta \in (1,2)$ 和分数阶的空间 Riesz 导数 $\alpha \in (1,2)$被认为。构建并分析了针对该问题的线性化交替方向隐式 (ADI) 方案。首先，我们使用经典的中心差分公式和一个新的$3-\beta$-阶公式分别在时间方向上近似二阶导数和卡普托导数。同时，应用中心差商和分数中心差公式来处理空间离散化。然后，证明了所提出的 ADI 方案无条件稳定并收敛于$3-\beta$-时间上的精度和空间上的二阶精度。此外，数值实验说明了 ADI 方案和理论结果的有效性。