Different kinds of boundary condition for time-fractional heat conduction equation

Different kinds of boundary conditions (Dirichlet, Neumann, Robin) for time-fractional heat conduction equation are discussed. The fundamental solutions to time-fractional heat conduction equation with the Caputo derivative of the order 0 <; α <; 2 is considered in a half-plane under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of the values of temperature and the values of its normal derivative and the physical condition with the prescribed linear combination of the values of temperature and the values of the heat flux at the boundary of the domain.