@prefix ns1: . @prefix ns2: . @prefix rdf: . @prefix rdfs: . @prefix xml: . @prefix xsd: . a ns1:ScholarlyArticle ; ns1:about , ; ns1:author ( ) ; ns1:citation , , , ; ns1:datePublished "2022-03-18" ; ns1:datePublishedReg "2022-03-18" ; ns1:description """Fractional differential equations have recently demonstrated their importance in a variety of fields, including medicine, applied sciences, and engineering. The main objective of this study is to propose an Adams-type multistep method for solving differential equations of fractional order. The method is developed by implementing the Lagrange interpolation and taking into account the idea of the Adams–Moulton method for fractional case. The fractional derivative applied in this study is in the Caputo derivative operator. The analysis of the proposed method is presented in terms of order of the method, order of accuracy, and convergence analysis, with the proposed method being proved to converge. The stability of the method is also examined, where the stability regions appear to be symmetric to the real axis for various values of α. In order to validate the competency of the proposed method, several numerical examples for solving linear and nonlinear fractional differential equations are included. The method will be presented in the numerical predict–correct technique for the condition where α∈(0,1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\alpha \\in (0,1)$\\end{document}, in which α represents the order of fractional derivatives of Dαy(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$D^{\\alpha }y(t)$\\end{document}.""" ; ns1:genre "article" ; ns1:isAccessibleForFree true ; ns1:isPartOf [ a ns1:PublicationVolume ; ns1:volumeNumber "2022" ], [ a ns1:PublicationIssue ; ns1:issueNumber "1" ], ; ns1:keywords "Adams-Moulton method", "Applied Sciences", "Caputo", "Caputo derivative operator", "Lagrange interpolation", "account", "accuracy", "analysis", "axis", "cases", "competencies", "conditions", "convergence analysis", "derivative operator", "derivatives", "differential equations", "engineering", "equations", "example", "field", "fractional case", "fractional derivative", "fractional differential equations", "fractional order", "idea", "importance", "interpolation", "main objective", "medicine", "method", "multistep methods", "nonlinear fractional differential equations", "numerical examples", "numerical solution", "objective", "operators", "order", "order of accuracy", "real axis", "region", "science", "solution", "stability", "stability region", "study", "technique", "terms", "terms of order", "values", "variety", "variety of fields" ; ns1:name "Numerical solution of fractional differential equations with Caputo derivative by using numerical fractional predict–correct technique" ; ns1:pagination "26" ; ns1:productId [ a ns1:PropertyValue ; ns1:name "dimensions_id" ; ns1:value "pub.1146389211" ], [ a ns1:PropertyValue ; ns1:name "doi" ; ns1:value "10.1186/s13662-022-03697-6" ] ; ns1:sameAs , ; ns1:sdDatePublished "2022-10-01T06:50" ; ns1:sdLicense "https://scigraph.springernature.com/explorer/license/" ; ns1:sdPublisher [ a ns1:Organization ; ns1:name "Springer Nature - SN SciGraph project" ] ; ns1:url "https://doi.org/10.1186/s13662-022-03697-6" ; ns2:license ; ns2:sdDataset "articles" . a ns1:DefinedTerm ; ns1:inDefinedTermSet ; ns1:name "Mathematical Sciences" . a ns1:DefinedTerm ; ns1:inDefinedTermSet ; ns1:name "Numerical and Computational Mathematics" . a ns1:Periodical ; ns1:issn "1687-1839", "2731-4235" ; ns1:name "Advances in Continuous and Discrete Models" ; ns1:publisher "Springer Nature" . a ns1:Person ; ns1:affiliation ; ns1:familyName "Ibrahim" ; ns1:givenName "Zarina Bibi" ; ns1:sameAs . a ns1:Person ; ns1:affiliation ; ns1:familyName "Zabidi" ; ns1:givenName "Nur Amirah" ; ns1:sameAs . a ns1:Person ; ns1:affiliation ; ns1:familyName "Kilicman" ; ns1:givenName "Adem" ; ns1:sameAs . a ns1:Person ; ns1:affiliation ; ns1:familyName "Majid" ; ns1:givenName "Zanariah Abdul" ; ns1:sameAs . a ns1:CreativeWork ; ns1:sameAs , . a ns1:CreativeWork ; ns1:sameAs , . a ns1:CreativeWork ; ns1:sameAs , . a ns1:CreativeWork ; ns1:sameAs , . a ns1:Organization ; ns1:alternateName "Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia", "Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia" ; ns1:name "Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia", "Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia" .