Thermo-diffusion effect on magnetohydrodynamics flow of fractional Casson fluid with heat generation and first order chemical reaction over a vertical plate

Abstract

Analytical solution of thermo diffusion effect on magnetohydrodynamics flow of fractionalized Casson
fluid over a vertical plate immersed in a porous media is obtained. Moreover, in the model of the problem, additional effects, like a chemical reaction, heat source/sink, and thermal radiation are also considered.
The model is solved by three approaches, namely, Atangana-Baleanu, Caputo-Fabrizio, and Caputo fractional
derivative of non-integer order γ. The governing dimensionless equations for temperatures, concentrations,
and velocities are solved using Laplace transform method and compared graphically. The effects of different parameters like fractional parameter γ, Thermo diffusion Sr, and magnetic parameter M are discussed
through numerous graphs. Furthermore, comparisons among ordinary and fractionalized velocity fields are
also drawn. It is found that the velocity obtained with Atangana-Baleanu fractional derivative is less than that
obtained by Caputo, Caputo-Fabrizio, or ordinary derivatives.