Comparison and analysis of the Atangana–Baleanu and Caputo–Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction

Abstract

Atangana and Baleanu (AB) in their recent work introduced a new version of fractional derivatives which uses the generalized Mittag-Leffler function as the non-singular and non-local kernel and accepts all properties of fractional derivatives. This articles aims to apply the AB fractional derivative to free convection flow of generalized Casson fluid due to the combined gradients of temperature and concentration with heat generation and first order chemical reaction. For the sake of comparison, this problem is also solved via Caputo-Fabrizio (CF) derivative technique. Exact solutions in both cases of AB and CF derivatives are obtained via Laplace transform and compared graphically as well as in tabular form. In the case of AB approach, the influence of pertinent parameters on velocity field is displayed in plots and discussed. It is found that for a unit time, the velocities obtained via AB and CF derivatives are identical. Velocities for the time less than 1 show little variation and for time bigger than 1, this variation increases. Keywords: Atangana-Baleanu and Caputo-Fabrizio fractional derivatives, Generalized Casson fluid, Heat generation, Chemical reaction