  We provide operator-norm convergence estimates for solutions to a
time-dependent equation of fractional elasticity in one spatial dimension, with
rapidly oscillating coefficients that represent the material properties of a
viscoelastic composite medium. Assuming periodicity in the coefficients, we
prove operator-norm convergence estimates for an operator fibre decomposition
obtained by applying to the original fractional elasticity problem the
Fourier--Laplace transform in time and Gelfand transform in space. We obtain
estimates on each fibre that are uniform in the quasimomentum of the
decomposition and in the period of oscillations of the coefficients as well as
quadratic with respect to the spectral variable. On the basis of these uniform
estimates we derive operator-norm-type convergence estimates for the original
fractional elasticity problem, for a class of sufficiently smooth densities of
applied forces.
