Solvability of a boundary value problem for a mixed-type equation with a partial Riemann-Liouville fractional derivative

We prove existence and uniqueness theorems for the solution of a nonlocal problem for a partial differential equation with a Riemann-Liouville fractional derivative in which the boundary condition contains a generalized fractional differentiation operator with the Gauss hypergeometric function in the kernel. We present a closed-form solution of the problem.