The behaviour of an isotropic homogeneous thermoelastic semi-infinite medium is investigated based on the acceleration of conductive and thermodynamic temperatures. A half-space x ≥ 0, under stress-free boundary condition at the near end, is considered. At this near end, a laser pulse decaying exponentially with time is applied. In the framework of fractional order generalized thermoelasticity theory, a one-dimensional coupled model is reduced using Laplace transform and corresponding thermally-induced temperature, stress and strain distribution functions are determined in the Laplace domain. Different inverse field functions are investigated numerically through a complex inversion formula of Laplace transform. The behavior of the field functions with different parameters are studied and presented graphically. Comparisons with the classical two temperature model are discussed.