ABSTRAC: The present paper deals with the review on the development of the theory of two-temperature thermoelasticity. The basic equations of two-temperature thermoelasticityin context of Lord and Shulman [6] theory and Green and Naghdi[15] theories of generalized thermoelasticity are reviewed. Relevant literature on two-temperature thermoelasticity is also reviewed.

Fractional differential equations arise in various fields of science and engineering such as rheology, fluid flows, electrical networks, viscoelasticity, chemical physics, biosciences, signal processing, systems control theory, electrochemistry, mechanics and diffusion processes. Fractional differential equations also serve as an excellent tool for the description of hereditary properties of va...

We use the Lagrange identity method and the logarithmic convexity to obtain uniqueness and exponential growth of solutions in the thermoelasticity of type III and thermoelasticity without energy dissipation. As this is not the first contribution of this kind in this theory, it is worth remarking that the assumptions we use here are different from those used in other previous contributions. We a...

In the present article, a comprehensive review of relevant literature is presented to highlight the role of fractional calculus in the field of thermoelasticity. This review is devoted to the generalizations of the classical heat conduction equation and formulation of associated theories of fractional thermoelasticity. The recently developed fractional order thermoelastic models are described w...

Integral boundary conditions for evolution problems have various applications in chemical engineering, thermoelasticity, underground water flow and population dynamics, see for example [16, 17, 24]. In fact, boundary value problems involving integral boundary conditions have received considerable attention, see for instance, [3, 10], [12]–[15], [18, 19, 26] and the references therein. In a rece...

A method used recently to obtain a discrete formalism for classical fields with nonlocal actions preserving chiral symmetry and uniqueness of fermion fields yields a discrete version of Huygens’ principle with free discrete propagators that recover their continuum forms in certain limit.

In this paper, a new theory of generalized micropolar thermoelasticity is derived by using fractional calculus. The generalized heat conduction equation in micropolar thermoelasticity has been modified with two distinct temperatures, conductive temperature and thermodynamic temperature by fractional calculus which depends upon the idea of the RiemannLiouville fractional integral operators. A un...

The wave propagation in viscothermoelastic materials is discussed the present work using nonlocal thermoelasticity model. This model was created Lord and Shulman generalized thermoelastic due to consequences of delay times formulations heat conduction motion equations. Eringen’s theory continuum. linear Kelvin–Voigt viscoelasticity explains viscoelastic properties isotropic material. analytical...