Convolutional Variational Principle, Reciprocal and Uniqueness Theorems in Linear Fractional Two-Temperature Thermoelasticity

Abstract

Two general models of fractional heat conduction law for non-homogeneous anisotropic elastic solid is introduced and the constitutive equations for the two-temperature fractional 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 restrictions imposed on the elasticity or thermal conductivity tensors except symmetry conditions. The two-temperature dynamic coupled, Lord-Shulman and fractional coupled thermoelasticity theories result as limit cases. The reciprocity relation in case of quiescent initial state is found to be independent of the order of differintegration.