  We propose an analytical model for the force-indentation relationship in
viscoelastic materials exhibiting a power law relaxation described by an
exponent n, where n = 1 represents the standard viscoelastic solid (SLS) model,
and n < 1 represents a fractional SLS model. To validate the model, we perform
nanoindentation measurements of poylacrylamide gels with atomic force
microscopy (AFM) force curves. We found exponents n < 1 that depends on the
bysacrylamide concentration. We also demonstrate that the fitting of AFM force
curves for varying load speeds can reproduce the dynamic viscoelastic
properties of those gels measured with dynamic force modulation methods.
