  We consider a space-fractional wave equation with a singular mass term
depending on the position and prove that it is very weak well-posed. The
uniqueness is proved in some appropriate sense. Moreover, we prove the
consistency of the very weak solution with classical solutions when they exist.
In order to study the behaviour of the very weak solution near the
singularities of the coefficient, some numerical experiments are conducted
where the appearance of a wall effect for the singular masses of the strength
of $\delta^2$ is observed.
