Numerous researchers have been drawn to the rheology of non-Newtonian fluids because of their diverse uses in the engineering and manufacturing fields, such as lubrication, plastic processing, and mining. Additionally, the characteristics of magnetohydrodynamics non-Newtonian fluids permit its widespread application in computer hard drives, loudspeakers, magnetic resonance imaging, the administration of magnetic medicines, and magnetic hyperthermia. The current work is focused on the analysis of heat and mass transfer in a magnetohydrodynamics Jeffrey nanofluid flows across a vertical plate because of these possible uses. Free convection, magnetic effect, and thermo-diffusion properties are all applied to the flow considered here. The modeling also takes into account the passive and active control of the Jeffrey nanofluid. Using suitable non-dimensional variables, ordinary differential equations are obtained from the modeling equations, and the Laplace transform method is used to solve these modeled equations. Semi-analytical solutions for temperature, concentration, and velocity are found after employing the Laplace transform approach to address the issue. For the distributions of velocity, concentration, and temperature, the inverted Laplace transform was obtained using the Zakian method. The concentration and temperature profiles are rising functions of the fractional and thermophoresis parameters, and they drop more quickly as the values of the Schmidt, Prandtl, and Nb (Brownian motion parameters) rise.