Abstract
In this work, the consideration of variable thermal conductivity as a linear function of temperature has been taken into account in the context of fractional order generalized thermoelasticity (Youssef's model). The governing equations have been derived and used to solve the one-dimensional problems of an elastic half-space. The solution has been induced in the Laplace transform domain and applying for thermal shock half-space on the bounding plane when it is rigid. The numerical inversion of the Laplace transform has been calculated numerically by using Tzou method and the results have been represented in figures with some comparisons to stand on the effect of the fractional order parameter and the variability of the thermal conductivity on all the studied fields.