Dirichlet problem for a nonlocal wave equation

We study the Dirichlet problem for a nonlocal wave equation in a rectangular domain. We prove the existence and uniqueness of a solution of the problem and show that determining whether the solution is unique can be reduced to determining whether a function of Mittag-Leffler type has real zeros. The obtained uniqueness condition turns into the uniqueness condition for the solution of the Dirichlet problem for the wave equation as the order of the fractional derivative in the equation tends to 2.

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