The authors deal with the application of fractional equations in physics. They consider the kinetic equation with fractional derivatives
where is a constant, and is the Riesz derivatives. The authors study the competition between normal diffusion and diffusion induced by fractional derivatives for (1). It is shown that for large times the fractional derivative term dominates the solution and leads to power type tails. Moreover a corresponding fractional generalization of the Ginzburg-Landau and nonlinear Schrödinger equations is proposed.