Thermoelastic diffusion with memory-dependent derivative

The constitutive equations are derived for the thermoelastic diffusion in anisotropic and isotropic solids, in the context of a new generalized thermoelasticity theory with two time delays and kernel functions. The coupled thermoelastic diffusion and the Lord–Shulman theories result from the given theory as particular cases. For anisotropic solid, the reciprocity theorem is proved; the convolutional variational principle is given and the uniqueness theorem based on the variational principle is proved.