Abstract In this study, the fractional model of thermo-viscoelasticity theory with variable thermal conductivity and rheological properties of the volume is considered to investigate bio-thermo-mechanics behavior in living tissue. The model is applied to a problem of cancerous layer with arbitrary thickness and its outer surface traction free. The bounding plane of the cancerous tissue is subjected to two different types of thermal loading; a non-Gaussian laser beam and harmonic heating. The problem is solved analytically by Kirchhoff and Laplace transformation. The exact solution in Laplace’s transform domain is obtained. Numerical results for the temperature, displacement, and stress distributions are given and illustrated graphically. The effects of time-fractional parameter and materials properties on the behavior of various fields are examined.

中文翻译：

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具有可变热材料特性的生物组织的分数热粘弹性响应

摘要 在本研究中，考虑了具有可变热导率和体积流变特性的热粘弹性理论的分数模型，以研究活组织中的生物热力学行为。该模型应用于任意厚度且外表面无牵引的癌变层问题。癌组织的边界平面受到两种不同类型的热负荷；非高斯激光束和谐波加热。该问题通过基尔霍夫和拉普拉斯变换解析解决。得到拉普拉斯变换域中的精确解。给出并以图形方式说明了温度、位移和应力分布的数值结果。