The paper primarily aims to examine the fractional effect and explore the impact of temperature-dependent properties and primary stress on reflecting plane and secondary vertically waves using the three-phase-lag model (THPL). Its problem has been formulated by neglecting the body force and external heat source and having initial stress and temperature-dependent under THPL theory in its fractional form (conformable fractional derivatives). The boundary conditions were applied taking into account mechanical stresses and temperature-dependence. A comparison between analytical and fractional solutions for the problem was made to get the solution included in the fractional orders. The authors analyzed the findings. They presented the findings graphically to illustrate the physical meaning of the issue under study. If the problem considered is in integer form, we strongly included that the results obtained agree with the results obtained by Abo-Dahab et al. (2020).

本文的主要目的是使用三相滞后模型（THPL）研究分数效应，并探索温度相关特性和主应力对反射平面波和次要垂直波的影响。通过忽略体力和外部热源，并根据THPL理论以分数形式（可变形分数导数）来确定初始应力和温度，从而解决了该问题。考虑到机械应力和温度依赖性，应用了边界条件。对该问题的解析解和分数解进行了比较，以使解决方案包含在分数阶中。作者分析了发现。他们以图形方式展示了研究结果，以说明所研究问题的物理含义。如果考虑的问题是整数形式，则我们强烈地认为所获得的结果与Abo-Dahab等人所获得的结果一致。（2020）。