BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS GLUING CONDITIONS FOR A FRACTIONAL ORDER PARABOLIC-ELLIPTIC-HYPERBOLIC EQUATION IN A RECTANGULAR DOMAIN

In this paper, we study a boundary value problem with discontinuous gluing conditions for a parabolic-elliptic-hyperbolic equation with a fractional order operator in the sense of Gerasimov-Caputo in a rectangular domain. A uniqueness criterion is established. A solution to the problem is constructed as a sum of a series in eigenfunctions of the corresponding one-dimensional spectral problem. Estimates are obtained that allow justification of the convergence of series in the class of regular solutions of this equation and the stability of the solution to the problem from the boundary data.