Boundary-value problem for a loaded hyperbolic-parabolic equation with degeneration of order

In this paper, we study a boundary-value problem with discontinuous conjugation conditions on the line of type changing for a model equation of mixed hyperbolic-parabolic type with order degeneration in the hyperbolicity domain. In the parabolic domain, the equation is the fractional diffusion equation, whereas in the hyperbolic domain it is the loaded one-speed transport equation. We prove the uniqueness and existence theorem and propose an explicit solution of the problem in the parabolic and hyperbolic domains.