The present investigation deals with the study of plane waves and the fundamental solution in rotating modified couple stress generalized thermoelastic solid with two-temperatures. The heat conduction equation with the fractional-order derivative and the formulation of the problem is applied in the context of the three-phase-lag model (3PHL), Green–Naghdi theory (G-N III) with energy dissipation and Green–Naghdi theory (G-N II) without energy dissipation. The medium is assumed initially stressed and normal mode analysis will be used to obtain the general solution for any set of boundary conditions. Some comparisons have been shown in figures to estimate the effects of the fractional-order, the hall current, rotation, and modified stress on all the studied fields.

本研究涉及平面波的研究以及具有两个温度的旋转修正偶应力广义热弹性固体的基本解。具有分数阶导数的热传导方程和问题的公式应用于三相滞后模型（3PHL）、具有能量耗散的格林-纳格迪理论（GN III）和格林-纳格迪理论（ GN II) 无能量耗散。假设介质最初受到应力，并且将使用正态模式分析来获得任何一组边界条件的一般解。图中显示了一些比较，以估计分数阶、霍尔电流、旋转和修正应力对所有研究领域的影响。