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.

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