Dirichlet problem for a non-local wave equation with a fractional derivative

We investigate the Dirichlet problem for a non-local wave equation with fractional derivative in rectangular domain. The equation under consideration turns into the wave equation when the order of fractional differentiation tends to two. The questions of existence and uniqueness for a regular solution are considered. In particular, we prove a criterion for solution uniqueness formulated in terms of linear sizes of the rectangular domain, which is an analogue of the classical result of D. G. Bourgin and R.Duffin for the wave equation.