<p>The paper studies an analog of the Frankl problem on the conjugation of two second-order hyperbolic type equations consisting of an inhomogeneous wave equation in one part and a degenerate hyperbolic equation of the first kind in the other part of the domain. For the investigated problem, a non-local boundary condition is given as a linear combination of the first-order derivative on one of the boundary characteristics of the wave equation and the fractional (in the sense of Riemann-Liouville) order derivative on the boundary characteristic of the degenerate hyperbolic equation. Using the method of integral equations, the solvability of the problem is equivalently reduced to the solvability of the weakly singular Volterra integral equation. The solution to the linear Volterra integral equation is known to be written out using the resolvent kernel. It is proved that the resolvent kernel series converges uniformly and that the solution belongs to the desired class. We also obtained sufficient conditions on the given functions ensuring that a singular regular exists in the considered domain of the problem studied. In some particular cases, the solution to the problem is found and written out in an explicit form.</p>