Fractional Model and Exact Solutions of Convection Flow of an Incompressible Viscous Fluid under the Newtonian Heating and Mass Diffusion

Figure 2

Concentration for different values of the order . We observe that when and the order of the Caputo derivative increases, the concentration of our considered model increases as well. In contrast, when , we notice the increase in the order of the fractional operator generates a decrease in the concentration. The previous behaviors are confirmed when the Schmidt number ; see Figures 2(a), and 2(b). Finally, the order of the Caputo derivative has an acceleration or retardation effect that depends on the considered times. These behaviors are explained by the accumulation of the memory effect when the order of the Caputo derivative increases.

(a)

(b)