Fractional Ginzburg–Landau equation for fractal media

Abstract

We derive the fractional generalization of the Ginzburg–Landau equation from the variational Euler–Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some simple solutions of the Ginzburg–Landau equation for fractal media are considered and different forms of the fractional Ginzburg–Landau equation or nonlinear Schrödinger equation with fractional derivatives are presented. The Agrawal variational principle and its generalization have been applied.