Boundary Value Problem for a Parabolic-hyperbolic Equation with a Reaction–diffusion Operator of Fractional Order

The work is devoted to the study of the unique solvability of a boundary value problem with a nonlinear gluing condition for a loaded reaction-diffusion-wave equation of fractional order. This problem is reduced to investigate of solvability of Fredholm type nonlinear integral equations. In proofing of the theorem on one valued solvability is used the method of successive approximations in combination it with the method of compressing mapping. The existence and uniqueness of the solution of the inverse boundary value problem are proved.