  One-dimensional Ginzburg-Landau equations with derivatives of noninteger
order are considered. Using psi-series with fractional powers, the solution of
the fractional Ginzburg-Landau (FGL) equation is derived. The leading-order
behaviours of solutions about an arbitrary singularity, as well as their
resonance structures, have been obtained. It was proved that fractional
equations of order $alpha$ with polynomial nonlinearity of order $s$ have the
noninteger power-like behavior of order $\alpha/(1-s)$ near the singularity.
