In this work, we derive a new fractional order theory for thermo-viscoelasticity. A uniqueness theorem for these equations is proved. A reciprocity theorem is also proved. A 1D problem for a viscoelastic half space is solved by using the Laplace transform technique. The solution in the transformed domain is obtained by a direct approach. The inverse transforms are obtained by using a numerical method. The temperature, displacement and stress distributions are computed and represented graphically.

中文翻译：

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热粘弹性分数阶理论及其应用

在这项工作中，我们推导出了热粘弹性的新的分数阶理论。证明了这些方程的唯一性定理。还证明了对等定理。通过使用拉普拉斯变换技术解决了粘弹性半空间的一维问题。变换域中的解是通过直接方法获得的。通过使用数值方法获得逆变换。计算温度，位移和应力分布并以图形方式表示。