Conformable Fractional Order Theory in Thermoelasticity

Abstract

The fractional heat conduction equation in thermoelasticity by the definitions of Riemann-Liouville and Caputo has some shortcomings. In this paper, we introduce a conformable fractional order theory of thermoelasticity that remedies this shortcoming. Firstly, we derive the heat conduction equation based on the conformable fractional derivative. Then, the theories of coupled thermoelasticity and of generalized thermoelasticity with one relaxation time follow as limit cases. Finally, we apply these new governing equations to the problem of the general thermo material. The analytical expressions for physical quantities are obtained using normal mode analysis in the physical domain. These expressions are numerically calculated and graphically illustrated for a given material. The findings were predicted and tested in the presence and absence of fractional parameter.