Viscoelasticity is an inherent property of the biological tissue and is often used as a diagnosis parameter in characterizing cancer. Recently, it has been found that fractional calculus agrees well with experimental results when describing the viscoelastic materials. In this study, the fractional linear thermo-viscoelastic theory is developed with considering the fractional relaxation effect of dual phase lag heat conduction model and viscoelastic constitutive relation simultaneously. The transient coupling thermal and mechanical behavior of biological tissue are investigated. The governing equations are solved by Laplace transformation. The effects of fractional parameter on the distributions of temperature, displacement and stress are obtained and illustrated graphically.

粘弹性是生物组织的固有特性，并且经常用作表征癌症的诊断参数。最近，已经发现分数微积分与描述粘弹性材料时的实验结果非常吻合。在本研究中，分数线性热粘弹性理论是在兼顾双相滞后热传导模型的分数弛豫效应和粘弹性本构关系的基础上发展起来的。研究了生物组织的瞬态耦合热力学行为。控制方程通过拉普拉斯变换求解。获得分数参数对温度，位移和应力分布的影响，并以图形方式说明。