Psi-Series Solution of Fractional Ginzburg-Landau Equation

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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 α/(1-s) near the singularity.