Abstract
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 prescribed linear combination of the values of temperature and the values of its normal derivative and the physical condition with prescribed linear combination of the values of temperature and the values of heat flux on the boundary of the domain. These two types of Robin boundary condition coincide only for the classical heat-conduction equation.
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