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The behaviour of a homogeneous and isotropic thermoelastic semi-infinite material is investigated based on the accelerations of the conductive and thermodynamical temperature. A half-space $x>0$ under stress free boundary condition at x = 0 and subjected to a thermal loading represented by a heavy sidestep function is considered. A one- dimensional system of equations in the framework of fractional order generalised thermoelasticity theory is considered as well. Laplace transform is used to get the solution in the Laplace domain. Thermally induced temperature, stress and strain distribution functions are determined in the Laplace domain. The Riemann-sum approximation method is used to obtain the different inverse field functions numerically. The behaviour of the stress, strain and the heat conductive temperature with the fractional-order parameter and time are investigated and presented graphically. Comparisons with the classical two-temperature models are discussed.

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