The time-fractional heat conduction equation with the Caputo derivative of the order is considered in a half-space in axisymmetric case 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.
Y. Z. Povstenko. "Axisymmetric Solutions to Time-Fractional Heat Conduction Equation in a Half-Space under Robin Boundary Conditions." Int. J. Differ. Equ. 2012 (SI2) 1 - 13, 2012. https://doi.org/10.1155/2012/154085