Abstract
Two general models of fractional heat conduction for non-homogeneous anisotropic elastic solids are introduced and the constitutive equations for thermoelasticity theory are obtained, uniqueness and reciprocal theorems are proved and the convolutional variational principle is established and used to prove a uniqueness theorem with no restriction on the elasticity or thermal conductivity tensors except for symmetry conditions. The dynamic coupled, Lord-Shulman, Green-Naghdi and fractional coupled thermoelasticity theories result as limit cases. The reciprocity relation in the case of quiescent initial state is found to be independent of the order of differintegration.