  The nonlinear theory of anomalous diffusion is based on particle interactions
giving an explicit microscopic description of diffusive processes leading to
sub-, normal, or super-diffusion as a result competitive effects between
attractive and repulsive interactions. We present the explicit analytical
solution to the nonlinear diffusion equation which we then use to compute the
correlation function which is experimentally measured by correlation
spectroscopy. The theoretical results are applicable in particular to the
analysis of fluorescence correlation spectroscopy of marked molecules in
biological systems. More specifically we consider the case of fluorescently
labeled lipids and we find that the nonlinear correlation spectrum reproduces
very well the experimental data indicating sub-diffusive molecular motion of
lipid molecules in the cell membrane.
