A Boundary-value Problem with Shift for a Hyperbolic Equation Degenerate in the Interior of a Region

For a degenerate hyperbolic equation in characteristic region (lune) a boundary-value problem with operators of fractional integro-differentiation is studied. The solution of this equation on the characteristics is related point-to-point to the solution and its derivative on the degeneration line. The uniqueness theorem is proved by the modified Tricomi method with inequality-type constraints on the known functions. Question of the problem solution’s existence is reduced to the solvability of a singular integral equation with Cauchy kernel of the normal type.