Fractional Ginzburg-Landau equations as generalizations of the classical one have been used to describe various physical phenomena. In this paper, we propose a numerical integration method for space fractional Ginzburg-Landau equations based on a dynamical low-rank approximation. We first approximate the space fractional derivatives by using a fractional centered difference method. Then, the resulting matrix differential equation is split into a stiff linear part and a nonstiff (nonlinear) one. For solving these two subproblems, a dynamical low-rank approach is employed. The convergence of our method is proved rigorously. Numerical examples are reported which show that the proposed method is robust and accurate.

作为经典方程的推广，分数阶 Ginzburg-Landau 方程已被用于描述各种物理现象。在本文中，我们提出了一种基于动态低秩逼近的空间分数阶 Ginzburg-Landau 方程的数值积分方法。我们首先使用分数中心差分法来近似空间分数阶导数。然后，将得到的矩阵微分方程分为刚性线性部分和非刚性（非线性）部分。为了解决这两个子问题，采用了动态低秩方法。我们的方法的收敛性得到了严格的证明。报告的数值例子表明所提出的方法是稳健和准确的。