The above table (Table 3) and Fig. 3. display the variations of stress\(\sigma_{\text{xx}}\) against the distance \(x\) for different values of the fractional parameters \(\alpha\) and \(\beta\). Also, Fig. 3, emphasizes that the depth of the stress for the models [, , SFLS, 2FDPL] is bigger than that for Lord-Shulman model. Furthermore, we observe that the values of the displacement converge to zero at \(x\)tends to 4, which agree with the considered regularity boundary conditions. Finally, Figs. (1-3) illustrate that the behavior of all studied fields changes rapidly for the modified fractional model 2FDPL (\(\alpha=0.75,\ \beta=0.75\)). Therefore, our modified model is the best and very useful for material science researchers and material designers.