Solutions to fractional diffusion-wave equation in a circular sector

The time-fractional diffusion-wave equation with the Caputo derivative of the order 0 < α ≤ 2 is considered in a domain 0 ≤ r < R, 0 < ϕ < ϕ0 under different boundary conditions. The Laplace integral transform with respect to time, the finite Fourier transforms with respect to the angular coordinate, and the finite Hankel transforms with respect to the radial coordinate are used. The fundamental solutions are expressed in terms of the Mittag-Leffler function. The particular cases of the obtained solutions corresponding to the diffusion equation (α = 1) and the wave equation (α = 2) coincide with those known in the literature.