Free convection flow of non-Newtonian fluids over flat, heated surfaces is an important natural phenomenon that also occurs in human-made engineering processes under various physical and mechanical situations. In the current study, the free convection magnetohydrodynamic flow of Jeffrey fluid with heat and mass transfer over an infinite vertical plate is examined. Mathematical modeling is performed using Fourier’s and Fick’s laws, and heat and momentum equations have been obtained. The non-dimensional partial differential equations for energy, mass, and velocity fields are determined using the Laplace transform method in a symmetric manner. Later on, the Laplace transform method is employed to evaluate the results for the temperature, concentration, and velocity fields with the support of Mathcad software. The governing equations, as well as the initial and boundary conditions, satisfy these results. The impacts of fractional and physical characteristics have been shown by graphical illustrations. The obtained fractionalized results are generalized by a more decaying nature. By taking the fractional parameter $\beta ,\gamma \to 1$, the classical results with the ordinary derivatives are also recovered, making this a good direction for symmetry analysis. The present work also has applications with engineering relevance, such as heating and cooling processes in nuclear reactors, the petrochemical sector, and hydraulic apparatus where the heat transfers through a flat surface. Moreover, the magnetized fluid is also applicable for controlling flow velocity fluctuations.