Fundamental solutions to Robin boundary-value problems for time-fractional heat conduction equation in a half-line

Анотація

The time-fractional heat conduction equation with the Caputo derivative of the order 0 < α ≤ 2 is considered in a half-line. Two types of Robin boundary condition are examined: the mathematical condition 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. These two types of Robin boundary condition coincide only in the case of classical heat conduction equation.