Abstract
The constitutive equations are given with a fractional Maxwell-Cattaneo heat conduction law using the Caputo fractional derivative and the fractional order heat transport equation is given. The uniqueness theorem is proved, the reciprocity relation is deduced and the variational characterization of solution is given. Seven thermoelasticity theories result from the given problem as special cases (Coupled, Lord-Shulman, phase-lag Green-Naghdi theories, Green-Naghdi theory without energy dissipation and the Green-Naghdi theory of type III).