Boundary value problem for partial differential equation with fractional Riemann–Liouville derivative

For a differential equation involving a fractional order diffusion equations, we study a non-local problem in an unbounded domain where the boundary condition involves a linear combination of generalized operators of a fractional integro-differentiation.
For various values of the parameters of these operators by Tricomi method we prove the uniqueness of solution to the considered problem. The existence of solution is obtained in the closed form as a solution to the appropriate equation with fractional derivative of various order.