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In the present paper, a new fractional model of fractional order thermo-viscoelasticity theory with and without energy dissipation is constructed. Some basic theorems can easily obtain in both theories. A three-dimensional model of fractional thermo-viscoelasticity is established. The model is applied to a specific problem of a half space subjected to harmonic heating and traction free surface. The reverses of Fourier transforms and Laplace processes are obtained numerically. Numerical results are given and illustrated graphically for temperature, displacement, and stress distributions. A comparison of coupled and generalized thermo-viscoelasticity theories are made.

Fractional thermo-viscoelasticity theory with and without energy dissipation