The Dirichlet problem for the generalized Laplace equation with fractional derivative

In the paper the Dirichlet problem for the generalized Laplace equation with fractional Riemann — Liouville derivative with respect to one of the two independent variables in the upper half-plane is investigated. The representation of the solution is found by the method of integral transformation with the Wright function in the core and the uniqueness theorem for the solution of the problem is proved by the method abc.