In this article, a novel mathematical model is theoretically developed by incorporating a memory-dependent derivative (MDD) into the temperature-rate-dependent thermoelasticity theory (Green–Lindsay) on three mathematical aspects in order to study the spatial behavior of the thermal signals in an isotropic, homogeneous, thermoelastic continuum. Firstly, to ensure the thermodynamic consistency of the proposed model, the constitutive equations involving MDD are derived from the principle of thermodynamics or continuum mechanics in conjunction with the corresponding kinematic assumptions. Secondly, to prove the finite propagation speeds of the thermal signals of the proposed model, a domain of influence theorem is established. Finally, to analyze the spatial propagation of the thermal signals inside the domain of influence, a spatial decay theorem is established. As an immediate outcome of this theoretical analysis, a uniqueness theorem of the proposed model is also derived.

中文翻译：

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具有记忆相关导数的广义热弹性中热信号的空间行为

在本文中，通过在三个数学方面将记忆相关导数 (MDD) 结合到温度速率相关热弹性理论 (Green-Lindsay) 中，从理论上开发了一种新的数学模型，以研究热信号的空间行为在各向同性、均匀、热弹性连续体中。首先，为保证所提出模型的热力学一致性，根据热力学或连续介质力学原理，结合相应的运动学假设，推导出涉及MDD的本构方程。其次，为了证明所提出模型的热信号的有限传播速度，建立了影响域定理。最后，为了分析影响域内热信号的空间传播，空间衰减定理成立。作为该理论分析的直接结果，还导出了所提出模型的唯一性定理。