Fractional analysis of unsteady magnetohydrodynamics Jeffrey flow over an infinite vertical plate in the presence of Hall current

The impact of Hall current on the multiphase thermal transfer of an incompressible electrically conductive Jeffrey flow over an infinitely vertical plate when heat absorption and chemical reaction are present has been examined. Partial differential equations have been used to describe the process, accounting for heat and mass transfer effects. This study uses extended Fourier's and Fick's laws together with the recently announced constant proportional Caputo (CPC) fractional operator. The fractional model is converted into a nondimensional form by applying some appropriate quantities. The nondimensional produced fractional model for momentum, heat, and diffusion equations based on the CPC fractional operator has been calculated semi‐analytically by applying the Laplace method. The Mathcad 15 software to sketch the graphs for several factors, like the Grashof number, mass Grashof number, Schmidt number, Prandtl number, Hall, and magnetic field parameters, is used to describe the velocity profile. Additionally, a graphical explanation is provided for the influence of the appeared parameters, particularly the effect of the fractional parameters. It is concluded that the result of the fluid model developed by the generalized constitutive relations is more accurate and generalized than the results of the artificially contracted fractional model. A fractional derivative is therefore the ideal option to achieve controlled concentration, temperature, and velocity. The current study is immediately relevant to geophysical, cosmically fluid dynamics, medical, biological, and any other processes that are significantly enhanced by a low gas density and a high magnetic field.