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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Main Authors: Naveed Iqbal, Moteb Fheed Saad Al Harbi, Saleh Alshammari, Shamsullah Zaland
Format: Article
Language:English
Published: Wiley 2022-01-01
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.
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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