Neumann boundary-value problems for a time-fractional diffusion-wave equation in a half-plane

The time-fractional diffusion-wave equation with the Caputo derivative of the order 0<α<20<α<2 is considered in a half-plane. Two types of Neumann boundary condition are examined: the mathematical condition with the prescribed boundary value of the normal derivative and the physical one with the prescribed boundary value of the matter flux.