  We study a system of partial differential equations with integer and
fractional derivatives arising in the study of forced oscillatory motion of a
viscoelastic rod. We propose a new approach considering a quotient of relations
appearing in the constitutive equation instead the constitutive equation
itself. Both, a rod and a body are assumed to have finite mass. The motion of a
body is assumed to be translatory. Existence and uniqueness for the
corresponding initial-boundary value problem is proved within the spaces of
functions and distributions.
