  Thermodynamically consistent fractional Burgers constitutive models for
viscoelastic media, divided into two classes according to model behavior in
stress relaxation and creep tests near the initial time instant, are coupled
with the equation of motion and strain forming the fractional Burgers wave
equations. Cauchy problem is solved for both classes of Burgers models using
integral transform method and analytical solution is obtained as a convolution
of the solution kernels and initial data. The form of solution kernel is found
to be dependent on model parameters, while its support properties implied
infinite wave propagation speed for the first class and finite for the second
class. Spatial profiles corresponding to the initial Dirac delta displacement
with zero initial velocity display features which are not expected in wave
propagation behavior.
