"articles" .
"fractional differential equations" .
_:Nfeb51d06189640b6bacfc45b0b00b28e "10.1186/s13662-022-03697-6" .
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"equations" .
_:Nfeb51d06189640b6bacfc45b0b00b28e .
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_:N5b10640ee6c6425084d0012e5e2b4a86 .
_:Ne123d1e8b35a4b989a483867098200a8 "Springer Nature - SN SciGraph project" .
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"article" .
_:N0dd5edeb121e45edb57ed0728328ad91 .
"Applied Sciences" .
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_:N6ab3711e65be43069864c0a881aeeacd .
"main objective" .
"Zanariah Abdul" .
"interpolation" .
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"Springer Nature" .
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"solution" .
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"engineering" .
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"stability" .
_:N46ada0a568cb45f9a734862a65cf51eb .
.
"2022-03-18" .
"stability region" .
"1687-1839" .
_:Nb703293450944ec8b19b9181794c08a1 .
"Caputo derivative operator" .
"Caputo" .
.
_:N5b10640ee6c6425084d0012e5e2b4a86 _:N0047c6ab3afe41a7acc368a5838ce236 .
"https://scigraph.springernature.com/explorer/license/" .
_:N0dd5edeb121e45edb57ed0728328ad91 "pub.1146389211" .
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"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\u2013Moulton 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 \u03B1. 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\u2013correct technique for the condition where \u03B1\u2208(0,1)\\documentclass[12pt]{minimal}\n \\usepackage{amsmath}\n \\usepackage{wasysym}\n \\usepackage{amsfonts}\n \\usepackage{amssymb}\n \\usepackage{amsbsy}\n \\usepackage{mathrsfs}\n \\usepackage{upgreek}\n \\setlength{\\oddsidemargin}{-69pt}\n \\begin{document}$\\alpha \\in (0,1)$\\end{document}, in which \u03B1 represents the order of fractional derivatives of D\u03B1y(t)\\documentclass[12pt]{minimal}\n \\usepackage{amsmath}\n \\usepackage{wasysym}\n \\usepackage{amsfonts}\n \\usepackage{amssymb}\n \\usepackage{amsbsy}\n \\usepackage{mathrsfs}\n \\usepackage{upgreek}\n \\setlength{\\oddsidemargin}{-69pt}\n \\begin{document}$D^{\\alpha }y(t)$\\end{document}." .
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"derivative operator" .
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_:Nb703293450944ec8b19b9181794c08a1 .
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.
.
_:Ne123d1e8b35a4b989a483867098200a8 .
"Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia" .
"Numerical and Computational Mathematics" .
"Numerical solution of fractional differential equations with Caputo derivative by using numerical fractional predict\u2013correct technique" .
_:Ne123d1e8b35a4b989a483867098200a8 .
.
_:Nb06ffda79b89446e9634f477533a1650 .
_:Nfeb51d06189640b6bacfc45b0b00b28e "doi" .
_:N46ada0a568cb45f9a734862a65cf51eb _:N6ab3711e65be43069864c0a881aeeacd .
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"fractional order" .
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"Ibrahim" .
"operators" .
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"study" .
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"accuracy" .
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"Kilicman" .
"variety of fields" .
"axis" .
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_:N0dd5edeb121e45edb57ed0728328ad91 .
"competencies" .
"Zarina Bibi" .
"Adem" .
"terms of order" .
"nonlinear fractional differential equations" .
"26" .
.
.
"derivatives" .
"order" .
_:Nb703293450944ec8b19b9181794c08a1 "2022" .
_:N0dd5edeb121e45edb57ed0728328ad91 "dimensions_id" .
"science" .
_:N0047c6ab3afe41a7acc368a5838ce236 _:N46ada0a568cb45f9a734862a65cf51eb .
"order of accuracy" .
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.
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"technique" .
_:Nb06ffda79b89446e9634f477533a1650 .
"https://doi.org/10.1186/s13662-022-03697-6" .
"Majid" .
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_:Nfeb51d06189640b6bacfc45b0b00b28e .
.
_:N5b10640ee6c6425084d0012e5e2b4a86 .
"analysis" .
"2731-4235" .
"2022-03-18" .
"Advances in Continuous and Discrete Models" .
"values" .
"importance" .