Analytical approach for the steady MHD conjugate viscous fluid flow in a porous medium with nonsingular fractional derivative

This study investigates the unsteady magnetohydrodynamics (MHD) flow of a viscous fluid. The fluid is passing over a vertical plate through porous medium. Additionally conjugate effects of heat and mass transfer with ramped temperatures, slip effect and influence of thermal radiation in the energy equation are taken into account. The dimensionless fractional-order governing equations, in the Caputo–Fabrizio sense, are solved with the help of Laplace transformation. Moreover, semi analytical technique is used to investigate the velocity field. Some results which present in literature are recovered as limiting cases. Influences of different parameters on the velocity profiles for the case of f(t)=t and f(t)=sinωt are highlighted. The novelty of the manuscript is the use of the most recent definition of the non integer order derivative operator i.e. Caputo–Fabrizio derivative operator, the use of generalized boundary conditions in terms of general function f(t), from our general results, several particular cases for instance when f(t) is a linear or sinusoidal function could be recovered.