Special function form exact solutions for Jeffery fluid: an application of power law kernel

Abstract This research note’s objective is to elaborate on the study of unsteady MHD natural convective flow Jeffery fluid with fractional derivative model. The phenomenon happens between two vertical parallel plates immersed in a porous medium. one plate moving time-dependent velocity $U_{0} f(t)$ U 0 f ( t ) , while other fixed. mathematical model presented system partial differential equation along physical conditions. Appropriate dimensionless variables are employed equations, and then this transformed into Caputo fractional-order solved analytically by Laplace transform. exact expressions for temperature, which satisfy imposed initial boundary conditions, obtained. Memory effects observed classical fails elaborate. Interesting results revealed from investigation emerging parameters as Grashof number, Prandtl relaxation time parameter, Hartmann porosity, parameter. elucidated detailed discussion assistance graphs. For sake validation results, corresponding solutions viscous fluids also obtained compared already existing literature.