Abstract
This article investigates the effects of the non-integer order derivative without singular kernel on the double convection MHD flow of a Casson fluid with and without a magnetic field and a porous medium over an oscillating vertical plate. The governing equations of the mass concentration, temperature distribution and velocity field have been converted using the Fabrizio-Caputo fractional derivative. The analytical solutions have been traced out for the mass concentration, temperature distribution and velocity field. The general solutions for the mass concentration, temperature distribution and velocity field have been expressed in terms of the newly defined Mittage-Leffler and Fox-H functions, respectively. Some similarities and differences have focused on the concentration, temperature and velocity by specifying a few emerging parameters for the fluid flow. Finally, a graphical illustration has been presented by employing the pertinent parameters of the fluid flow, and it is noted that the ordinary and Caputo-Fabrizio fractional fluid models have a reciprocal behavior for the fluid flow. (C) 2017 Published by Elsevier B.V.