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 model equation mixed hyperbolic-parabolic degeneration order in hyperbolicity domain. parabolic domain, is fractional diffusion equation, whereas hyperbolic domain it loaded one-speed transfer equation. We prove uniqueness and existence theorem propose an explicit solution domains.