Abstract
In this work, we present a new thermoelasticity model in the context of the new theory of fractional order strain thermoelasticity with variable thermal conductivity. The thermoelastic properties of a semi-infinite homogeneous isotropic medium with variable thermal conductivity were investigated. The governing equations have been derived and we use the direct method to obtain the solutions of the field functions in the Laplace domain. The medium is subjected to ramp type thermal loading. To obtain the different inverse field functions numerically we used a complex inversion formula of Laplace transform based on a Fourier expansion. The effects of different parameters on the conductive temperature, the thermodynamical temperature, the displacement the stress and on the strain distribution are presented graphically. Comparison between each field function with constant and variable thermal conductivity are also presented graphically and discussed.