Analytical Investigation of Nonlinear Fractional Harry Dym and Rosenau-Hyman Equation via a Novel Transform

We use a new integral transform approach to solve the fractional Harry Dym equation and fractional Rosenau-Hyman equation in this work. The Elzaki transform and the integral transformation are combined in the suggested method (ET). To handle two nonlinear problems, we first construct the Elzaki tran...

Full description

Saved in:
Bibliographic Details
Published in:Journal of function spaces 2022, Vol.2022, p.1-12
Main Authors: Alshammari, Saleh, Iqbal, Naveed, Yar, Mohammad
Format: Article
Language:English
Subjects:
Calculus
Control theory
Convergence
Decomposition
Differential equations
Error analysis
Exact solutions
Fractional calculus
Integral transforms
Mathematical analysis
Partial differential equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c366t-cf7960bf458f1bc0534751faf4cb3c53d5b7cae72c047167d9c5221d3bdf29103
cites cdi_FETCH-LOGICAL-c366t-cf7960bf458f1bc0534751faf4cb3c53d5b7cae72c047167d9c5221d3bdf29103
container_end_page 12
container_issue
container_start_page 1
container_title Journal of function spaces
container_volume 2022
creator Alshammari, Saleh
Iqbal, Naveed
Yar, Mohammad
description We use a new integral transform approach to solve the fractional Harry Dym equation and fractional Rosenau-Hyman equation in this work. The Elzaki transform and the integral transformation are combined in the suggested method (ET). To handle two nonlinear problems, we first construct the Elzaki transforms of the Caputo fractional derivative (CFD) and Atangana-Baleanu fractional derivative (ABFD). The ultimate purpose of this study is to find an error analysis that demonstrates that our final result converges to the exact and approximate result. The convergent series form solution demonstrates the method’s efficiency in resolving several types of fractional differential equations. Furthermore, the solutions obtained in this study agree well with the exact solutions; thus, this strategy is powerful and efficient as an alternate way for obtaining approximate solutions to both linear and nonlinear fractional differential equations.
doi_str_mv 10.1155/2022/8736030
format article
fullrecord <record><control><sourceid>proquest_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_cae6424dd05c4140b4af856096334c63</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><doaj_id>oai_doaj_org_article_cae6424dd05c4140b4af856096334c63</doaj_id><sourcerecordid>2715335977</sourcerecordid><originalsourceid>FETCH-LOGICAL-c366t-cf7960bf458f1bc0534751faf4cb3c53d5b7cae72c047167d9c5221d3bdf29103</originalsourceid><addsrcrecordid>eNp9kU9LJDEQxYPsgjJ68wMEPO72mv-ZPoqrzoAoiHsO1UlHM_YkmsyM9Lc3sy0ezSEpil-9Iu8hdErJH0qlPGeEsfO55opwcoCOGKeimdfz46tu1SE6KWVFCKG0pULKI_RyEWEYN8HCgJdx15dNeIJNSBEnj-9SHELsIePrDHbfrdQCch7x33GNITr8kEofYdssxjVEfPW2nYZ3ATDU-V0_4McMsfiU18fop4eh9Cef7wz9u756vFw0t_c3y8uL28ZypTaN9bpVpPNCzj3tLJFcaEk9eGE7biV3stMWes0sEZoq7VorGaOOd86zlhI-Q8tJ1yVYmdcc1pBHkyCY_42Unwzk-uWhN1VHCSacI9IKKkgnwM-lIq3iXNh6zdDZpPWa09u22mNWaZurD8UwTSXnstW6Ur8nyuZUSu7911ZKzD4ds0_HfKZT8V8T_hyig_fwPf0BkTSN1g</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2715335977</pqid></control><display><type>article</type><title>Analytical Investigation of Nonlinear Fractional Harry Dym and Rosenau-Hyman Equation via a Novel Transform</title><source>Publicly Available Content (ProQuest)</source><source>Wiley Open Access</source><creator>Alshammari, Saleh ; Iqbal, Naveed ; Yar, Mohammad</creator><contributor>Gurefe, Yusuf</contributor><creatorcontrib>Alshammari, Saleh ; Iqbal, Naveed ; Yar, Mohammad ; Gurefe, Yusuf</creatorcontrib><description>We use a new integral transform approach to solve the fractional Harry Dym equation and fractional Rosenau-Hyman equation in this work. The Elzaki transform and the integral transformation are combined in the suggested method (ET). To handle two nonlinear problems, we first construct the Elzaki transforms of the Caputo fractional derivative (CFD) and Atangana-Baleanu fractional derivative (ABFD). The ultimate purpose of this study is to find an error analysis that demonstrates that our final result converges to the exact and approximate result. The convergent series form solution demonstrates the method’s efficiency in resolving several types of fractional differential equations. Furthermore, the solutions obtained in this study agree well with the exact solutions; thus, this strategy is powerful and efficient as an alternate way for obtaining approximate solutions to both linear and nonlinear fractional differential equations.</description><identifier>ISSN: 2314-8896</identifier><identifier>EISSN: 2314-8888</identifier><identifier>DOI: 10.1155/2022/8736030</identifier><language>eng</language><publisher>New York: Hindawi</publisher><subject>Calculus ; Control theory ; Convergence ; Decomposition ; Differential equations ; Error analysis ; Exact solutions ; Fractional calculus ; Integral transforms ; Mathematical analysis ; Partial differential equations</subject><ispartof>Journal of function spaces, 2022, Vol.2022, p.1-12</ispartof><rights>Copyright © 2022 Saleh Alshammari et al.</rights><rights>Copyright © 2022 Saleh Alshammari et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c366t-cf7960bf458f1bc0534751faf4cb3c53d5b7cae72c047167d9c5221d3bdf29103</citedby><cites>FETCH-LOGICAL-c366t-cf7960bf458f1bc0534751faf4cb3c53d5b7cae72c047167d9c5221d3bdf29103</cites><orcidid>0000-0001-9604-1680 ; 0000-0003-3846-0128 ; 0000-0002-8548-7078</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/2715335977/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2715335977?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,4010,25731,27900,27901,27902,36989,44566,75096</link.rule.ids></links><search><contributor>Gurefe, Yusuf</contributor><creatorcontrib>Alshammari, Saleh</creatorcontrib><creatorcontrib>Iqbal, Naveed</creatorcontrib><creatorcontrib>Yar, Mohammad</creatorcontrib><title>Analytical Investigation of Nonlinear Fractional Harry Dym and Rosenau-Hyman Equation via a Novel Transform</title><title>Journal of function spaces</title><description>We use a new integral transform approach to solve the fractional Harry Dym equation and fractional Rosenau-Hyman equation in this work. The Elzaki transform and the integral transformation are combined in the suggested method (ET). To handle two nonlinear problems, we first construct the Elzaki transforms of the Caputo fractional derivative (CFD) and Atangana-Baleanu fractional derivative (ABFD). The ultimate purpose of this study is to find an error analysis that demonstrates that our final result converges to the exact and approximate result. The convergent series form solution demonstrates the method’s efficiency in resolving several types of fractional differential equations. Furthermore, the solutions obtained in this study agree well with the exact solutions; thus, this strategy is powerful and efficient as an alternate way for obtaining approximate solutions to both linear and nonlinear fractional differential equations.</description><subject>Calculus</subject><subject>Control theory</subject><subject>Convergence</subject><subject>Decomposition</subject><subject>Differential equations</subject><subject>Error analysis</subject><subject>Exact solutions</subject><subject>Fractional calculus</subject><subject>Integral transforms</subject><subject>Mathematical analysis</subject><subject>Partial differential equations</subject><issn>2314-8896</issn><issn>2314-8888</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNp9kU9LJDEQxYPsgjJ68wMEPO72mv-ZPoqrzoAoiHsO1UlHM_YkmsyM9Lc3sy0ezSEpil-9Iu8hdErJH0qlPGeEsfO55opwcoCOGKeimdfz46tu1SE6KWVFCKG0pULKI_RyEWEYN8HCgJdx15dNeIJNSBEnj-9SHELsIePrDHbfrdQCch7x33GNITr8kEofYdssxjVEfPW2nYZ3ATDU-V0_4McMsfiU18fop4eh9Cef7wz9u756vFw0t_c3y8uL28ZypTaN9bpVpPNCzj3tLJFcaEk9eGE7biV3stMWes0sEZoq7VorGaOOd86zlhI-Q8tJ1yVYmdcc1pBHkyCY_42Unwzk-uWhN1VHCSacI9IKKkgnwM-lIq3iXNh6zdDZpPWa09u22mNWaZurD8UwTSXnstW6Ur8nyuZUSu7911ZKzD4ds0_HfKZT8V8T_hyig_fwPf0BkTSN1g</recordid><startdate>2022</startdate><enddate>2022</enddate><creator>Alshammari, Saleh</creator><creator>Iqbal, Naveed</creator><creator>Yar, Mohammad</creator><general>Hindawi</general><general>Hindawi Limited</general><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>ATCPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M7S</scope><scope>P62</scope><scope>PATMY</scope><scope>PHGZM</scope><scope>PHGZT</scope><scope>PIMPY</scope><scope>PKEHL</scope><scope>PQEST</scope><scope>PQGLB</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>PYCSY</scope><scope>Q9U</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0001-9604-1680</orcidid><orcidid>https://orcid.org/0000-0003-3846-0128</orcidid><orcidid>https://orcid.org/0000-0002-8548-7078</orcidid></search><sort><creationdate>2022</creationdate><title>Analytical Investigation of Nonlinear Fractional Harry Dym and Rosenau-Hyman Equation via a Novel Transform</title><author>Alshammari, Saleh ; Iqbal, Naveed ; Yar, Mohammad</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c366t-cf7960bf458f1bc0534751faf4cb3c53d5b7cae72c047167d9c5221d3bdf29103</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Calculus</topic><topic>Control theory</topic><topic>Convergence</topic><topic>Decomposition</topic><topic>Differential equations</topic><topic>Error analysis</topic><topic>Exact solutions</topic><topic>Fractional calculus</topic><topic>Integral transforms</topic><topic>Mathematical analysis</topic><topic>Partial differential equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Alshammari, Saleh</creatorcontrib><creatorcontrib>Iqbal, Naveed</creatorcontrib><creatorcontrib>Yar, Mohammad</creatorcontrib><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Agricultural &amp; Environmental Science</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East &amp; Africa Database</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>ProQuest Engineering Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Environmental Science Database</collection><collection>ProQuest Central (New)</collection><collection>ProQuest One Academic (New)</collection><collection>Publicly Available Content (ProQuest)</collection><collection>ProQuest One Academic Middle East (New)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Applied &amp; Life Sciences</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection><collection>Environmental Science Collection</collection><collection>ProQuest Central Basic</collection><collection>Directory of Open Access Journals</collection><jtitle>Journal of function spaces</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Alshammari, Saleh</au><au>Iqbal, Naveed</au><au>Yar, Mohammad</au><au>Gurefe, Yusuf</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analytical Investigation of Nonlinear Fractional Harry Dym and Rosenau-Hyman Equation via a Novel Transform</atitle><jtitle>Journal of function spaces</jtitle><date>2022</date><risdate>2022</risdate><volume>2022</volume><spage>1</spage><epage>12</epage><pages>1-12</pages><issn>2314-8896</issn><eissn>2314-8888</eissn><abstract>We use a new integral transform approach to solve the fractional Harry Dym equation and fractional Rosenau-Hyman equation in this work. The Elzaki transform and the integral transformation are combined in the suggested method (ET). To handle two nonlinear problems, we first construct the Elzaki transforms of the Caputo fractional derivative (CFD) and Atangana-Baleanu fractional derivative (ABFD). The ultimate purpose of this study is to find an error analysis that demonstrates that our final result converges to the exact and approximate result. The convergent series form solution demonstrates the method’s efficiency in resolving several types of fractional differential equations. Furthermore, the solutions obtained in this study agree well with the exact solutions; thus, this strategy is powerful and efficient as an alternate way for obtaining approximate solutions to both linear and nonlinear fractional differential equations.</abstract><cop>New York</cop><pub>Hindawi</pub><doi>10.1155/2022/8736030</doi><tpages>12</tpages><orcidid>https://orcid.org/0000-0001-9604-1680</orcidid><orcidid>https://orcid.org/0000-0003-3846-0128</orcidid><orcidid>https://orcid.org/0000-0002-8548-7078</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 2314-8896
ispartof Journal of function spaces, 2022, Vol.2022, p.1-12
issn 2314-8896
2314-8888
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_cae6424dd05c4140b4af856096334c63
source Publicly Available Content (ProQuest); Wiley Open Access
subjects Calculus
Control theory
Convergence
Decomposition
Differential equations
Error analysis
Exact solutions
Fractional calculus
Integral transforms
Mathematical analysis
Partial differential equations
title Analytical Investigation of Nonlinear Fractional Harry Dym and Rosenau-Hyman Equation via a Novel Transform
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-24T02%3A07%3A40IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_doaj_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Analytical%20Investigation%20of%20Nonlinear%20Fractional%20Harry%20Dym%20and%20Rosenau-Hyman%20Equation%20via%20a%20Novel%20Transform&rft.jtitle=Journal%20of%20function%20spaces&rft.au=Alshammari,%20Saleh&rft.date=2022&rft.volume=2022&rft.spage=1&rft.epage=12&rft.pages=1-12&rft.issn=2314-8896&rft.eissn=2314-8888&rft_id=info:doi/10.1155/2022/8736030&rft_dat=%3Cproquest_doaj_%3E2715335977%3C/proquest_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c366t-cf7960bf458f1bc0534751faf4cb3c53d5b7cae72c047167d9c5221d3bdf29103%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2715335977&rft_id=info:pmid/&rfr_iscdi=true