## 8 Physical Analysis of Results  
After performing the fractional simulations, the physical reflection of the parameters is presented in this section. For assessing the physical dynamic, numerical values were assigned to physical parameters, such as \(Pr=6.2,\ \varphi=0.02,\ t=1.0,\ \alpha=0.5,\ \beta=0.5,\)\(Pr=2.4,\ Gr=2.4,\ \theta=\frac{\pi}{4},\ w=0.9,\ b=0.4,\ \text{and}\ \delta=\frac{\pi}{4}.\) Figures 3-7 illustrate the impacts of various parameters on the velocity and temperature field dynamics. It was remarked that, for nonlocal derivatives, we could analyze only one profile at \(\alpha,\ \beta=1,\) but with the virtue of fractional-order derivative models, more than one profile of the subsequent problems could be analyzed. Moreover, the non-integer-order derivatives models could explain different layers for flowing fluid. Furthermore, due to this advantage of fractional models, the comparisons of different fluid layers could be examined individually. Figure 3 presents the comparative analysis of the velocity profile against the water and kerosene-oil base fluid with the suspension of copper oxide and silver nanoparticles. The water-based nanofluid showed more enhancement in the velocity profile compared to the kerosene-oil-based nanoparticle. Furthermore, the nanofluid mixed with copper oxide \(\ \left(CuO\right)\\) nanoparticles had a more significant impact on the velocity compared to the silver \(\ \left(Ag\right)\\) nanoparticles. Figure 4 reports the changes in velocity for \(\alpha\) and \(\beta.\) An increasing influence of velocity due to both factors was observed. The influence of the volume fraction parameter, \(\varphi,\ \text{on}\\) velocity is highlighted Figure 5. The declining velocity change was noted for increasing the volume fraction parameter. The effects  
The comparison of different nanofluids and nanoparticles for the thermal profile is plotted in Figure 7a. It is clear from the figure that the kerosene-oil-based nanofluid had a greater tendency to enhance the thermal conductivity than the water-based nanofluid. Figure 7b illustrates the impact of the Prandtl number, \(Pr\), on the temperature profile. A falling behavior of the temperature profile can be seen against a larger Prandtl constant. Physically, with the increment in \(\Pr\) values, the thermal forces were weakened. Figure 7c aims to present the thermal aspect of the fractional parameters \(\alpha\) and \(\beta\) on the temperature profile. The temperature profile rose for fractional parameters \(\alpha\) and \(\beta\). Table 2 aims to address the numerical fluctuations in the velocity and temperature profile by using the [PERSON] [31] and [PERSON]'s [32] integration tools. The lower temperature rate due to a larger space parameter, \(\xi\), was noted. However, the velocity increased for larger \(\xi\) values using both techniques. After careful inspection, it was noted that the numerical results obtained via [PERSON]'s [32] technique had better relative convergence compared to [PERSON]'s [31] tools. Table 3 presents the numerical values of the Nusselt number and the wall shear force. With an increment in \(\xi\), the Nusselt number decreased, while an increasing impact of skin friction was observed. Figure 5: Change in velocity for \(\varphi\). Figure 6: Change in velocity for \(M\).