Abstract
In this study, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in the context of the fractional order generalized thermoelasticity theory. The medium is assumed initially quiescent. Laplace and Fourier transform techniques are used to obtain the general solution for any set of boundary conditions. The general solution is applied to a specific problem of a half-space subjected to thermal shock. The inverse Fourier transforms are obtained analytically, while the inverse Laplace transforms are computed numerically. Some comparisons have been shown in figures to estimate the effect of the fractional order on all the studied fields.