Analysis of Fractional Differential Equations with the Help of Different Operators
This study uses an Elzaki decomposition method with two fractional derivatives to solve a fractional nonlinear coupled system of Whitham-Broer-Kaup equations. For the fractional derivatives, we used Caputo and Atangana-Baleanu derivatives in the Caputo manner. Furthermore, the proposed techniques ar...
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Format: | Article |
Language: | English |
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Wiley
2022-01-01
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Series: | Advances in Mathematical Physics |
Online Access: | http://dx.doi.org/10.1155/2022/1333109 |
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author | Naveed Iqbal Moteb Fheed Saad Al Harbi Saleh Alshammari Shamsullah Zaland |
author_facet | Naveed Iqbal Moteb Fheed Saad Al Harbi Saleh Alshammari Shamsullah Zaland |
author_sort | Naveed Iqbal |
collection | DOAJ |
description | This study uses an Elzaki decomposition method with two fractional derivatives to solve a fractional nonlinear coupled system of Whitham-Broer-Kaup equations. For the fractional derivatives, we used Caputo and Atangana-Baleanu derivatives in the Caputo manner. Furthermore, the proposed techniques are compared to the solutions of other renowned analytical methods, including the Adomian decomposition technique, variation iteration technique, and homotopy perturbation technique. We used two nonlinear problems to illustrate the accuracy and validity of the proposed approaches. The results of numerical simulations were used to verify that the proposed methods are accurate and efficient, and the results are displayed in graphs and tables. The obtained results demonstrate that the algorithm is very real, simple to apply, and effective in investigating the nature of complicated nonlinear models in science and engineering. |
format | Article |
id | doaj-art-7d0f98d5ac1a405888d761756945bd05 |
institution | Kabale University |
issn | 1687-9139 |
language | English |
publishDate | 2022-01-01 |
publisher | Wiley |
record_format | Article |
series | Advances in Mathematical Physics |
spelling | doaj-art-7d0f98d5ac1a405888d761756945bd052025-02-03T01:30:02ZengWileyAdvances in Mathematical Physics1687-91392022-01-01202210.1155/2022/1333109Analysis of Fractional Differential Equations with the Help of Different OperatorsNaveed Iqbal0Moteb Fheed Saad Al Harbi1Saleh Alshammari2Shamsullah Zaland3Department of MathematicsDepartment of MathematicsDepartment of MathematicsFaculty of MathematicsThis study uses an Elzaki decomposition method with two fractional derivatives to solve a fractional nonlinear coupled system of Whitham-Broer-Kaup equations. For the fractional derivatives, we used Caputo and Atangana-Baleanu derivatives in the Caputo manner. Furthermore, the proposed techniques are compared to the solutions of other renowned analytical methods, including the Adomian decomposition technique, variation iteration technique, and homotopy perturbation technique. We used two nonlinear problems to illustrate the accuracy and validity of the proposed approaches. The results of numerical simulations were used to verify that the proposed methods are accurate and efficient, and the results are displayed in graphs and tables. The obtained results demonstrate that the algorithm is very real, simple to apply, and effective in investigating the nature of complicated nonlinear models in science and engineering.http://dx.doi.org/10.1155/2022/1333109 |
spellingShingle | Naveed Iqbal Moteb Fheed Saad Al Harbi Saleh Alshammari Shamsullah Zaland Analysis of Fractional Differential Equations with the Help of Different Operators Advances in Mathematical Physics |
title | Analysis of Fractional Differential Equations with the Help of Different Operators |
title_full | Analysis of Fractional Differential Equations with the Help of Different Operators |
title_fullStr | Analysis of Fractional Differential Equations with the Help of Different Operators |
title_full_unstemmed | Analysis of Fractional Differential Equations with the Help of Different Operators |
title_short | Analysis of Fractional Differential Equations with the Help of Different Operators |
title_sort | analysis of fractional differential equations with the help of different operators |
url | http://dx.doi.org/10.1155/2022/1333109 |
work_keys_str_mv | AT naveediqbal analysisoffractionaldifferentialequationswiththehelpofdifferentoperators AT motebfheedsaadalharbi analysisoffractionaldifferentialequationswiththehelpofdifferentoperators AT salehalshammari analysisoffractionaldifferentialequationswiththehelpofdifferentoperators AT shamsullahzaland analysisoffractionaldifferentialequationswiththehelpofdifferentoperators |