Generalized boundary conditions for time-fractional heat conduction equation

Different types of boundary conditions for the time-fractional heat conduction equation in a bounded domain are examined. A composed solid consisting of three domains is considered. Assuming that the thickness of the intermediate domain is small with respect to two other sizes and is constant, a three-dimensional heat conduction problem in the intermediate domain is reduced to the two-dimensional one for the median surface endowed with averaged physical properties. The obtained results can be interpreted as the generalized conditions of nonperfect thermal contact.