Theory of Generalized Piezoporo Thermoelasticity

Generalized Theory of Micropolar-fractional-ordered Thermoelasticity with Two-temperature

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...

Thermoelasticity and generalized thermoelasticity viewed as wave hierarchies

It is seen how to write the standard form of the four partial differential equations in four unknowns of anisotropic thermoelasticity as a single equation in one variable, in terms of isothermal and isentropic wave operators. This equation, of diffusive type, is of the eighth order in the space derivatives and seventh order in the time derivatives and so is parabolic in character. After having ...

Fractional order generalized thermoelasticity theories: A review

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...

Numerical modeling of generalized nonlinear system arising in thermoelasticity

In this paper, the Adomian decomposition method (ADM) is presented for finding numerical solution of fractional nonlinear system arising in thermoelasticity. The derivatives are understood in the Caputo sense. The reason of using fractional order differential equations (FOD) is that FOD are naturally related to systems with memory which exists in most biological systems. Also they are closely r...

On (non-)exponential decay in generalized thermoelasticity with two temperatures

We study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the nonexponential stability for the Lord-Shulman model.

Variations Formulations of the Coupled Theory of Linear Thermoelasticity