Abstract
In this work, the influence of fractional-order derivative with two relaxation times in a thermoelastic medium under laser pulse is established. The surface of the half-space with free stresses is considered to be heated by a laser pulse. The exact analytical solution is adopted for the variations of temperature as well as the components of displacement and stress. Based on the eigen-values approach and Laplace transform, the solutions of all variables have been obtained analytically. The results were graphically represented to show the erect of laser pulse in order to display the physical meaning of the phenomena. The graphical results indicate that the influence of fractional-order parameter plays an important role on all distributions.