On a Problem for the Third Order Equation with Parabolic-Hyperbolic Operator Including a Fractional Derivative

This work devoted to one valued solvability of a local problem for a parabolic-hyperbolic type differential equation of third order involving Gerasimov-Caputo fractional operator. Boundary value problem, involving third boundary condition on the parabolic domain and discontinuous gluing condition on the line x = 0, is considered. The problem replaced by Volterra type nonlinear integral equations. The existence of solution is proved by the method of successive approximations of factorial law.