A comparative study of Atangana-Baleanu and Caputo-Fabrizio fractional derivatives to the convective flow of a generalized Casson fluid

Abstract

Based on exponential kernel, Caputo and Fabrizio suggested a new definition for fractional order derivatives in 2015. Recently, in 2016, Atangana and Baleanu proposed another version of fractional derivatives, which uses the generalized Mittag-Leffler function as the non-singular and non-local kernel. Moreover, the Atangana-Balaenu (AB) version has all properties of fractional derivatives. Therefore, this articles aims to use the AB fractional derivative idea for the first time to study the free convection flow of a generalized Casson fluid due to the combined gradients of temperature and concentration. Hence, heat and mass transfer are considered together. For the sake of comparison, this problem is also solved via the Caputo-Fabrizio (CF) derivatives technique. Exact solutions in both cases (AB and CF derivatives) are obtained via the 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 unit time, the velocities obtained via AB and CF derivatives are identical. Velocities for time less than 1 show little variation and, for time higher than 1, this variation increases.