The novel numerical solutions for Caputo-Fabruzo fractional  Newell–Whitehead–SegelEquation by using Aboodh-ADM

The novel numerical solutions for Caputo-Fabruzo fractional Newell–Whitehead–SegelEquation by using Aboodh-ADM | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The novel numerical solutions for Caputo-Fabruzo fractional Newell–Whitehead–SegelEquation by using Aboodh-ADM Mehmet Merdan, Yasin Şahin, Pınar Açıkgöz This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4287125/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This article aims to solve Caputo-Fabruzo fractional differential equations using the Aboodh transform together with the Adomian Decomposition method (A-ADM). Since the Aboodh transform can only be applied to linear equations, ADM is an effective technique for approximating solutions of nonlinear differential equations. In nonlinear systems, the Newell-Whitehead-Segel equation plays an important role, explaining the emergence of stripes in 2-dimensional systems. The findings show that the results obtained from the tables provide superior results compared to the existing conformable q-Shehu homotopy analysis transform method (Cq-SHATM) in the literature. With the help of Matlab package program, numerical values were found to depict three-dimensional surfaces and displayed in a table. Caputo-Fabruzo fractional fractional Newell–Whitehead–Segel Equation Aboodh Transform Method Adomian Decomposition method Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4287125","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":294433319,"identity":"2ebfe967-ac45-4bfb-b2c3-24df8b8c67d1","order_by":0,"name":"Mehmet Merdan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/UlEQVRIiWNgGAWjYLACHgYGOTCDsQEiIEGMFmN0LQYEtSQ2EK1Fd9rhYx/e1NxJnx+RnSb5c4ddHj8D88HbPAx/8nFpMbudljxzzrFnuRtv5G6T5j2TXCzZwJZszcNgYNmAU0uOMTMP2+HcjTOAWhjbmBM3HOAxkwZqwekys9v5n5l5/h1ONwRqkfzZVp+4/wD/NwJacpiZedsOJ8hL5G6TADISNzDwsBHQkmbMOLfvsOEGnrebrXnbjifOOMxmbDnHwBiPluTHDG++HZaXb8/dePNnW3Vif3vzwxtvKuQIRAwQGByAsZjBXIIaGBjkG4hQNApGwSgYBSMTAABSG1Tx/BMsXAAAAABJRU5ErkJggg==","orcid":"","institution":"","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Mehmet","middleName":"","lastName":"Merdan","suffix":""},{"id":294433320,"identity":"77b39bfa-4274-4458-baaa-a1192a08a61d","order_by":1,"name":"Yasin Şahin","email":"","orcid":"","institution":"","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yasin","middleName":"","lastName":"Şahin","suffix":""},{"id":294433321,"identity":"1090b606-2c59-4ae0-8760-706080226848","order_by":2,"name":"Pınar Açıkgöz","email":"","orcid":"","institution":"","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Pınar","middleName":"","lastName":"Açıkgöz","suffix":""}],"badges":[],"createdAt":"2024-04-18 10:38:42","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4287125/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4287125/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":56711335,"identity":"6f97c628-2599-4939-a275-caa5537814f0","added_by":"auto","created_at":"2024-05-18 14:51:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":446961,"visible":true,"origin":"","legend":"","description":"","filename":"ThenovelnumericalsolutionsforCaputoFabruzofractionalNewellWhiteheadSegel.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4287125/v1_covered_3967f8b4-91e5-4b59-95e0-87b38cc2e470.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The novel numerical solutions for Caputo-Fabruzo fractional Newell–Whitehead–SegelEquation by using Aboodh-ADM","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Caputo-Fabruzo fractional, fractional Newell–Whitehead–Segel Equation, Aboodh Transform Method, Adomian Decomposition method","lastPublishedDoi":"10.21203/rs.3.rs-4287125/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4287125/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis article aims to solve Caputo-Fabruzo fractional differential equations using the Aboodh transform together with the Adomian Decomposition method (A-ADM). Since the Aboodh transform can only be applied to linear equations, ADM is an effective technique for approximating solutions of nonlinear differential equations. In nonlinear systems, the Newell-Whitehead-Segel equation plays an important role, explaining the emergence of stripes in 2-dimensional systems. The findings show that the results obtained from the tables provide superior results compared to the existing conformable q-Shehu homotopy analysis transform method (Cq-SHATM) in the literature. With the help of Matlab package program, numerical values were found to depict three-dimensional surfaces and displayed in a table.\u003c/p\u003e","manuscriptTitle":"The novel numerical solutions for Caputo-Fabruzo fractional Newell–Whitehead–SegelEquation by using Aboodh-ADM","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-24 21:34:05","doi":"10.21203/rs.3.rs-4287125/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ab7a1c03-f0d4-4050-a54e-d40ab5fadf79","owner":[],"postedDate":"April 24th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-05-18T14:43:14+00:00","versionOfRecord":[],"versionCreatedAt":"2024-04-24 21:34:05","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4287125","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4287125","identity":"rs-4287125","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}