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

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

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...

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Main Authors: Nadeem Ahmad Sheikh, Farhad Ali, Muhammad Saqib, Ilyas Khan, Syed Aftab Alam Jan, Ali Saleh Alshomrani, Metib Said Alghamdi
Format: Article
Language:English
Published: Elsevier 2017-01-01
Series:Results in Physics
Online Access:http://www.sciencedirect.com/science/article/pii/S221137971630571X
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spelling doaj-c9bd77c4ae35443abbbe00175a5bbe2d2020-11-25T02:06:25ZengElsevierResults in Physics2211-37972017-01-017789800Comparison and analysis of the Atangana–Baleanu and Caputo–Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reactionNadeem Ahmad Sheikh0Farhad Ali1Muhammad Saqib2Ilyas Khan3Syed Aftab Alam Jan4Ali Saleh Alshomrani5Metib Said Alghamdi6Department of Mathematics, City University of Science and Information Technology, Peshawar 25000, PakistanDepartment of Mathematics, City University of Science and Information Technology, Peshawar 25000, Pakistan; Corresponding author.Department of Mathematics, City University of Science and Information Technology, Peshawar 25000, PakistanBasic Engineering Sciences Department, College of Engineering Majmaah University, Majmaah 11952, Saudi ArabiaDepartment of Mathematics, City University of Science and Information Technology, Peshawar 25000, PakistanDepartment of Mathematics, Faculty of Science, King Abdul Aziz University, Jeddah 21577, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences, Jazan University, 45 142, Saudi ArabiaAtangana 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 reactionhttp://www.sciencedirect.com/science/article/pii/S221137971630571X
collection DOAJ
language English
format Article
sources DOAJ
author Nadeem Ahmad Sheikh
Farhad Ali
Muhammad Saqib
Ilyas Khan
Syed Aftab Alam Jan
Ali Saleh Alshomrani
Metib Said Alghamdi
spellingShingle Nadeem Ahmad Sheikh
Farhad Ali
Muhammad Saqib
Ilyas Khan
Syed Aftab Alam Jan
Ali Saleh Alshomrani
Metib Said Alghamdi
Comparison and analysis of the Atangana–Baleanu and Caputo–Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction
Results in Physics
author_facet Nadeem Ahmad Sheikh
Farhad Ali
Muhammad Saqib
Ilyas Khan
Syed Aftab Alam Jan
Ali Saleh Alshomrani
Metib Said Alghamdi
author_sort Nadeem Ahmad Sheikh
title Comparison and analysis of the Atangana–Baleanu and Caputo–Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction
title_short Comparison and analysis of the Atangana–Baleanu and Caputo–Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction
title_full Comparison and analysis of the Atangana–Baleanu and Caputo–Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction
title_fullStr Comparison and analysis of the Atangana–Baleanu and Caputo–Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction
title_full_unstemmed Comparison and analysis of the Atangana–Baleanu and Caputo–Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction
title_sort comparison and analysis of the atangana–baleanu and caputo–fabrizio fractional derivatives for generalized casson fluid model with heat generation and chemical reaction
publisher Elsevier
series Results in Physics
issn 2211-3797
publishDate 2017-01-01
description 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
url http://www.sciencedirect.com/science/article/pii/S221137971630571X
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