Abstract A subspace $\Cal D'_{\ast}(P)$ of the
space of distributions has been analized and the Laplace transform of their
elements applied to solve, in a prescribed domain, the system of linear
partial differential equations with fractional derivatives, as well. To this
system belongs a mathematical model of a visco elastic rod submited to the
axial force of the form $F(t)=B+A\theta (tt_0)$, where $A$ and $B$
are constants and $\theta$ is the Heaviside functions.
