  Fractional Ginzburg-Landau equations as the generalization of the classical
one have been used to describe various physical phenomena. In this paper, we
propose a numerical integration method for solving 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 used. The convergence of our
method is proved rigorously. Numerical examples are reported which show that
the proposed method is robust and accurate.
