  We study a class of nonlinear fractional differential equations with multiple
delays, which is represented by the Voigt creep fractional model of
viscoelasticity. We discuss two Voigt models, the first being linear and the
second being nonlinear. The linear Voigt model give us the physical
interpretation and is associated with important results since the creep
function characterizes the viscoelastic behavior of stress and strain. For the
nonlinear model of Voigt, our theoretical study and analysis provides existence
and stability, where time delays are expressed in terms of Boltzmann's
superposition principle. By means of the Banach contraction principle, we prove
existence of a unique solution and investigate its continuous dependence upon
the initial data as well as Ulam stability. The results are illustrated with an
example.
