Analysis of the heat and mass transfer in the MHD flow of a generalized Casson fluid in a porous space via non-integer order derivatives without a singular kernel

- The heat and mass transfer is studied in a generalized Casson fluid.
- The fluid is considered in terms of MHD and passes through a porous medium.
- The problem is modelled using the Fabrizio-Caputo fractional derivative definition.
- The general solutions are obtained in terms of the Mittage- Leffler and Fox-H functions.
- The results are discussed for rheological parameters graphically.

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.