Ginzburg-Landau (GL) dynamics are popular interacting particle systems. Macroscopic fluctuations theory (MFT) is now considered as the cornerstone of non-equilibrium statistical mechanics for diffusive systems. In this talk I will consider GL dynamics with long range interactions so that the system is superdiffusive and hydrodynamic limits are given by (non-linear) fractional diffusion equations. I will discuss issues concerning the establishment of a MFT for these GL dynamics. Joint work with R. Chetrite, P. Gonçalves and M. Jara.