Unique solvability of a non-local problem for mixed-type equation with fractional derivative

In this work, we investigate a boundary problem with non-local conditions for mixed parabolic-hyperbolic-type equation with three lines of type changing with Caputo fractional derivative in the parabolic part. We equivalently reduce considered problem to the system of second kind Volterra integral equations. In the parabolic part, we use solution of the first boundary problem with appropriate Green's function, and in hyperbolic parts, we use corresponding solutions of the Cauchy problem. Copyright (c) 2016 John Wiley & Sons, Ltd.