  Classical and thermodynamically consistent fractional Burgers models are
examined in creep and stress relaxation tests. Using the Laplace transform
method, the creep compliance and relaxation modulus are obtained in integral
form, that yielded, when compared to the thermodynamical requirements, the
narrower range of model parameters in which the creep compliance is a Bernstein
function while the relaxation modulus is completely monotonic. Moreover, the
relaxation modulus may even be oscillatory function with decreasing amplitude.
The asymptotic analysis of the creep compliance and relaxation modulus is
performed near the initial time-instant and for large time as well.
