Fractional Heat Conduction and Related Theories of Thermoelasticity

General balance equations and constitutive equations coupled the temperature field and solid deformation are considered. Time- and space-nonlocal generalizations of the standard Fourier lawFourier law, the corresponding generalizations of the classical heat conduction equation and formulation of associated theories of fractional thermoelasticity are discussed. Different kinds of boundary conditionsBoundary condition for the time-fractional heat conduction equation are analyzed including the Dirichlet, mathematical and physical Neumann and Robin conditions, the conditions of perfect thermal contactPerfect thermal contact and the moving interface boundary conditions at the solid–liquid interface. Representations of stresses in terms of the displacement potentialDisplacement potential, biharmonic Galerkin vectorGalerkin vector and biharmonic Love function are given.