On a Nonlocal Boundary Value Problem for a Degenerate Parabolic-Hyperbolic Equation with Fractional Derivative

The goal of this work is to study the existence and uniqueness of the solution to a nonlocal boundary value problem for a degenerate differential equation of mixed type. A parabolic-hyperbolic equation with a fractional Gerasimov–Caputo derivative is considered. The uniqueness of the solution is proved by the integral energy method using the some properties of hypergeometric functions and integro-differential operators of fractional order. The existence of the solution is proved by the method of integral equations.