arXiv:nlin/0606070v1 [nlin.SI] 28 Jun 2006 Journal of Physics A. Vol.39. No.26. (2006) pp.8395-8407. Psi-Series Solution of Fractional Ginzburg-Landau Equation Vasily E. Tarasov Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119992, Russia E-mail: tarasov@theory.sinp.msu.ru Abstract One-dimensional Ginzburg-Landau equations with derivatives of noninteger or- der are considered. Using psi-series with fractional powers, the solution of the frac- tional 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 α with polynomial nonlinearity of order s have the noninteger power-like behavior of order α/(1 − s) near the singularity. PACS numbers: 05.45.-a; 45.10.Hj 1 Introduction Differential equations that contain derivatives of noninteger order [1, 2] are called frac- tional equations [3, 4]. The interest to fractional equations has been growing continually during the last few years because of numerous applications. In a fairly short period of time the areas of applications of fractional calculus have become broad. For example, the derivatives and integrals of fractional order are used in chaotic dynamics [5, 6], material sciences [7, 8, 9], mechanics of fractal and complex media [10, 11], quantum mechan- ics [12, 13], physical kinetics [5, 14, 15, 16], plasma physics [17, 18], astrophysics [19], long-range dissipation [20], non-Hamiltonian mechanics [21, 22], long-range interaction [23, 24, 25], anomalous diffusion and transport theory [5, 26, 27]. 1