Solvability of a Non-local Problem with Integral Transmitting Condition for Mixed Type Equation with Caputo Fractional Derivative

In the present paper, we discuss solvability questions of a non-local problem with integral form transmitting conditions for a mixed parabolic–hyperbolic type equation with the Caputo fractional derivative in a domain bounded by smooth curves. A uniqueness of the solution for a formulated problem we prove using energy integral method with some modifications. The existence of solution will be proved by equivalent reduction of the studied problem into a system of second kind Fredholm integral equations.