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 $F(t)=B+A\theta (t-t_0)$, where $A$ and $B$ are constants and $\theta$ is the Heaviside functions.