We study transversal vibrations of an elastic axially compressed rod on a fractional derivative type of viscoelastic foundation. We assume that the axial force has a constant and a time dependent part given by Dirac distributions. The dynamics of the system is described by a system of two partial differential equations, having integer and fractional derivatives. The solution of this system is obtained in the space of distributions and its asymptotic behavior is investigated. It is shown that the foundation increases the stability bound. AMS Mathematics Subject Classification (2000) 74H45.