Abstract
In this work, a model of two-temperature fractional order generalized thermoelasticity for an elastic half-space with constant elastic parameters has been constructed. Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem of a half-space subjected to thermal shock and moving heat source with constant velocity. The inverse Laplace transforms are computed numerically and some comparisons have been shown in figures to estimate the effect of each of the heat source velocity and the fractional order parameter.