On the Dirichlet problem for the generalized Laplace equation

This paper considers the Dirichlet problem for a second-order partial differential equation with the Riemann-Liouville derivative with respect to one of two independent order variables, less than two, in the upper half-plane. The equation under study turns into a two-dimensional Laplace equation if the order of the fractional derivative coincides with an integer. The main result of this work is the proof of theorems on the existence and uniqueness of a solution to the problem posed. An explicit form of representation of the solution is obtained. Сorresponding asymptotic estimates аre given.