Abstract
In the current investigation, the thermoelasticity with a model of fractional order is used to discuss a problem of thermoelastic half-space. Such theory depends on the time-fractional derivative of Caputo of order alpha. The thermal conductivity is considered to be a variable, and the medium surface is subjected to a free from traction and a thermal shock. Then, the transform of Laplace has been utilized for the solutions of the governing equations. The inverse of the Laplace transform entertained numerically, employing a technique based on methods of Fourier expansion. The obtained numerical solutions for different variables and the obtained results are offered graphically. The effect of the variation of thermal conductivity as well as a fractional-order parameter on displacement, temperature, and stress are studied. A comparison is made between the results obtained in the current investigation and the previous results by others when the new parameters neglect. The results obtained indicated to the significant role of the heat conduction fractional model, thermal conductivity, temperature dependent, and thermal relaxation time on the thermoelastic half-space.