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

By N. Sheikh, Farhad Ali, Muhammad Saqib, Ilyas Khan, Syed Aftab Alam Jan, Ali Saleh Alshomrani, Metib Alghamdi. 2017

216 citations recorded by the source corpus.

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.

Subfields: Biomedical Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ad5ee345fe4edf5629d6631b006b9adfce911647

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Citations in the corpus

Numerical approximation of Riemann‐Liouville definition of fractional derivative: From Riemann‐Liouville to Atangana‐Baleanu (2018, methodology): “Numerous articles have been published, among them: Chua’s circuit model [34], mechanics and heat transfer of Casson fluid [35, 36] and the Allen Cahn model [37].”
European Vanilla Option Pricing Model of Fractional Order without Singular Kernel (2018, methodology): “[24] used the analysis of the Atangana–Baleanu (AB) and CF for generalized Casson fluid model.”
Comparing the new fractional derivative operators involving exponential and Mittag-Leffler kernel (2020, result): “[22, 23, 16] are some comparison studies based on the CFO and ABO.”
New aspects of time fractional optimal control problems within operators with nonsingular kernel (2020, methodology): “On the other hand, Casson fluid has been modeled in [52].”