Unsteady MHD flow of Maxwell fluid with Caputo–Fabrizio non-integer derivative model having slip/non-slip fluid flow and Newtonian heating at the boundary

The purpose of this manuscript is to investigate the unsteady magnetohydrodynamics flow of a Maxwell fluid with conjugate effects of heat and mass transfer under the slip and non-slip conditions at the boundary. Moreover, we apply the Caputo–Fabrizio fractional derivative to model the proposed problem. We consider the fluid in a porous medium over a vertical plate with ramped temperature. We take into consideration the influence of thermal radiation in the energy equations. We solve the governing equations by Laplace transform technique, and we use the Stehfest’s algorithm to find the inverse Laplace transform. Hence, we obtain the semianalytical solutions for temperature, concentration and velocity in case of ramped temperature as well as for both slip and non-slip conditions and general motion of the plate. We demonstrate the numerical results by some figures.