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.

中文翻译：

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有和没有能量耗散的分数热粘弹性理论

在本文中，建立了一个新的分数阶热粘弹性理论的分数模型，有和没有能量耗散。在这两种理论中都可以很容易地得到一些基本定理。建立了分数热粘弹性三维模型。该模型适用于半空间受谐波加热和牵引自由表面的特定问题。傅立叶变换和拉普拉斯过程的逆是通过数值方法获得的。给出了温度、位移和应力分布的数值结果并以图形方式说明。对耦合和广义热粘弹性理论进行了比较。