In the current investigation, we introduce a generalized modified model of thermoviscoelasticity with different fractional orders. Based on the Kelvin–Voigt model and generalized thermoelasticity theory with multi-phase-lags, the governing system equations are derived. In limited cases, the proposed model is reduced to several previous models in the presence and absence of fractional derivatives. The model is then adopted to investigate a problem of an isotropic spherical cavity, the inner surface of which is exposed to a time-dependent varying heat and constrained. The system of governing differential equations has been solved analytically by applying the technique of Laplace transform. To clarify the effects of the fractional-order and viscoelastic parameters, we depicted our numerical calculations in tables and figures. Finally, the results obtained are discussed in detail and also confirmed with those in the previous literature.

在当前的研究中，我们介绍了具有不同分数阶的热粘弹性的广义修正模型。基于Kelvin-Voigt模型和具有多相滞后的广义热弹性理论，推导了控制系统方程。在有限的情况下，在存在和不存在分数导数的情况下，将建议的模型简化为多个先前的模型。然后采用该模型来研究各向同性球形空腔的问题，该球形空腔的内表面暴露于随时间变化的热量并受到约束。应用拉普拉斯变换技术已经解析地解决了控制微分方程的系统。为了阐明分数阶和粘弹性参数的影响，我们在表和图中描述了数值计算。最后，