  Recently, a non-linear model of viscoelasticity based on Rational Extended
Thermodynamics was proposed in [arXiv:2312.05116]. This theory extends the
evolution of the viscous stress beyond the linear framework of the Maxwell
model to the non-linear realm, provided that the viscous energy function is
given. This work aims at establishing a possible constitutive law for the
viscous energy such that the relaxation modulus of the fractional Maxwell model
of order $\alpha \in (1/2, 1]$ is contained within the solutions of the
(non-linear) relaxation experiment. Necessary and sufficient conditions for the
existence of this coincident solution are discussed, together with a numerical
evaluation of the viscous energy associated with the non-linear model.
