Abstract
The extended thermoelastic theory with fractional derivative is described in this article to estimate temperature variation, displacement components, and stress components in two-dimensional orthotropic materials. In the Laplace domain, exact solutions are found. The physical quantities are calculated analytically using Laplace and Fourier transforms and the eigenvalues approaches. The Laplace-Fourier transform inversion procedures are carried out using numerical approaches. The numerical outcome for all the physical quantities investigated are introduced and shown visually. In this case, if the fractional parameter is equal to one and the thermal relaxation time is equal to zero, then the Lord and Shulman (LS) theory comes into play and the classical dynamical coupled (CT) theory comes in. Also, the comparison between the orthotropic medium and isotropic medium are presented.