The existence of complex environments is associated with the phenomenon of anomalous diffusion where, in particular, relevant correlation functions have power law decays with time, in contrast to the classical Brownian motion. The interior of a protein provides an illustration of such an irregular medium, and the existence of subdiffusive processes has been investigated in the context of protein dynamics using various techniques, such as fluorescence correlation spectroscopy, neutron scattering or in an NMR perspective focusing on spin relaxation. We combine approaches based on the fractional Fokker-Planck, of the generalized Langevin equation to provide tools to interpret protein dynamics in the contexts of NMR and neutron scattering experiments.