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In this paper, a theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of heat conduction with fractional orders. The obtained general solution is applied to a specific problem of a medium, semi-infinite solid considered to be made of a homogeneous thermoelastic material. The bounding plane surface of the medium is being subjected to a non-Gaussian laser pulse. The medium is assumed initially quiescent and Laplace transforms techniques will be used to obtain the general solution for any set of boundary conditions. The inverse of the Laplace transforms are computed numerically using a method based on Fourier’s expansion techniques. The theories of coupled thermoelasticity and of generalized thermoelasticity with one relaxation time follow as limit cases. Some comparisons have been shown in figures to estimate the effects of the fractional order, temperature discrepancy, laser-pulse and the laser intensity parameters on all the studied fields.