Forced oscillations of a body attached to a viscoelastic rod of fractional derivative type

We study forced oscillations of a rod with a body attached to its free end so that the motion of a system is described by two sets of equations, one of integer and the other of the fractional order. To the constitutive equation we associate a single function of complex variable that plays a key role in finding the solution of the system and in determining its properties. This function could be defined for a linear viscoelastic bodies of integer/fractional derivative type.