Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators

This paper aims to implement an analytical method, known as the Laplace homotopy perturbation transform technique, for the result of fractional-order Whitham–Broer–Kaup equations. The technique is a mixture of the Laplace transformation and homotopy perturbation technique. Fractional derivatives wit...

Full description

Saved in:
Bibliographic Details
Main Authors: Kamsing Nonlaopon, Muhammad Naeem, Ahmed M. Zidan, Rasool Shah, Ahmed Alsanad, Abdu Gumaei
Format: Article
Language:English
Published: Wiley 2021-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2021/7979365
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850170641626431488
author Kamsing Nonlaopon
Muhammad Naeem
Ahmed M. Zidan
Rasool Shah
Ahmed Alsanad
Abdu Gumaei
author_facet Kamsing Nonlaopon
Muhammad Naeem
Ahmed M. Zidan
Rasool Shah
Ahmed Alsanad
Abdu Gumaei
author_sort Kamsing Nonlaopon
collection DOAJ
description This paper aims to implement an analytical method, known as the Laplace homotopy perturbation transform technique, for the result of fractional-order Whitham–Broer–Kaup equations. The technique is a mixture of the Laplace transformation and homotopy perturbation technique. Fractional derivatives with Mittag-Leffler and exponential laws in sense of Caputo are considered. Moreover, this paper aims to show the Whitham–Broer–Kaup equations with both derivatives to see their difference in a real-world problem. The efficiency of both operators is confirmed by the outcome of the actual results of the Whitham–Broer–Kaup equations. Some problems have been presented to compare the solutions achieved with both fractional-order derivatives.
format Article
id doaj-art-9aa184515d0c4b06a1fc4ece1fdaff6a
institution OA Journals
issn 1076-2787
1099-0526
language English
publishDate 2021-01-01
publisher Wiley
record_format Article
series Complexity
spelling doaj-art-9aa184515d0c4b06a1fc4ece1fdaff6a2025-08-20T02:20:26ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/79793657979365Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel OperatorsKamsing Nonlaopon0Muhammad Naeem1Ahmed M. Zidan2Rasool Shah3Ahmed Alsanad4Abdu Gumaei5Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDeanship of Joint First Year Umm Al-Qura University, Makkah, Saudi ArabiaDepartment of Mathematics, College of Science, King Khalid University, Abha 9004, Saudi ArabiaDepartment of Mathematics, Abdul Wali University Mardan, Mardan, PakistanSTC’s Artificial Intelligent Chair, Department of Information Systems, College of Computer and Information Sciences, King Saud University, Riyadh 11451, Saudi ArabiaSTC’s Artificial Intelligent Chair, Department of Information Systems, College of Computer and Information Sciences, King Saud University, Riyadh 11451, Saudi ArabiaThis paper aims to implement an analytical method, known as the Laplace homotopy perturbation transform technique, for the result of fractional-order Whitham–Broer–Kaup equations. The technique is a mixture of the Laplace transformation and homotopy perturbation technique. Fractional derivatives with Mittag-Leffler and exponential laws in sense of Caputo are considered. Moreover, this paper aims to show the Whitham–Broer–Kaup equations with both derivatives to see their difference in a real-world problem. The efficiency of both operators is confirmed by the outcome of the actual results of the Whitham–Broer–Kaup equations. Some problems have been presented to compare the solutions achieved with both fractional-order derivatives.http://dx.doi.org/10.1155/2021/7979365
spellingShingle Kamsing Nonlaopon
Muhammad Naeem
Ahmed M. Zidan
Rasool Shah
Ahmed Alsanad
Abdu Gumaei
Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators
Complexity
title Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators
title_full Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators
title_fullStr Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators
title_full_unstemmed Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators
title_short Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators
title_sort numerical investigation of the time fractional whitham broer kaup equation involving without singular kernel operators
url http://dx.doi.org/10.1155/2021/7979365
work_keys_str_mv AT kamsingnonlaopon numericalinvestigationofthetimefractionalwhithambroerkaupequationinvolvingwithoutsingularkerneloperators
AT muhammadnaeem numericalinvestigationofthetimefractionalwhithambroerkaupequationinvolvingwithoutsingularkerneloperators
AT ahmedmzidan numericalinvestigationofthetimefractionalwhithambroerkaupequationinvolvingwithoutsingularkerneloperators
AT rasoolshah numericalinvestigationofthetimefractionalwhithambroerkaupequationinvolvingwithoutsingularkerneloperators
AT ahmedalsanad numericalinvestigationofthetimefractionalwhithambroerkaupequationinvolvingwithoutsingularkerneloperators
AT abdugumaei numericalinvestigationofthetimefractionalwhithambroerkaupequationinvolvingwithoutsingularkerneloperators