SOLVING FRACTIONAL DIFFUSION AND FRACTIONAL DIFFUSION-WAVE EQUATIONS BY PETROV-GALERKIN FINITE ELEMENT METHOD

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dc.authoridEsen, Alaattin/0000-0002-7927-5941
dc.authoridYAĞMURLU, Nuri Murat/0000-0003-1593-0254
dc.authoridUÇAR, Yusuf/0000-0003-1469-5002
dc.authorwosidEsen, Alaattin/ABE-5694-2021
dc.authorwosidEsen, Alaattin/F-2415-2016
dc.authorwosidYAĞMURLU, Nuri Murat/AAB-8514-2020
dc.authorwosidUÇAR, Yusuf/ABG-8562-2020
dc.contributor.authorEsen, A.
dc.contributor.authorUcar, Y.
dc.contributor.authorYagmurlu, M.
dc.contributor.authorTasbozan, O.
dc.date.accessioned2024-08-04T21:01:10Z
dc.date.available2024-08-04T21:01:10Z
dc.date.issued2014
dc.departmentİnönü Üniversitesien_US
dc.description.abstractIn the last few years, it has become highly evident that fractional calculus has been widely used in several areas of science. Because of this fact, their numerical solutions also have become urgently important. In this manuscript, numerical solutions of both the fractional diffusion and fractional diffusion-wave equations have been obtained by a Petrov-Galerkin finite element method using quadratic B-spline base functions as trial functions and linear B-spline base functions as the test functions. In those equations, fractional derivatives are used in terms of the Caputo sense. While the L1 discretizaton formula has been applied to fractional diffusion equation, the L2 discretizaton formula has been applied to the fractional diffusion-wave equation. Finally, the error norms L-2 and L-infinity have been calculated for testing the accuracy of the proposed scheme.en_US
dc.identifier.endpage168en_US
dc.identifier.issn2146-1147
dc.identifier.issue2en_US
dc.identifier.startpage155en_US
dc.identifier.urihttps://hdl.handle.net/11616/104155
dc.identifier.volume4en_US
dc.identifier.wosWOS:000218996900003en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.language.isoenen_US
dc.publisherTurkic World Mathematical Socen_US
dc.relation.ispartofTwms Journal of Applied and Engineering Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectFinite element methoden_US
dc.subjectPetrov-Galerkin methoden_US
dc.subjectFractional diffusion equationen_US
dc.subjectFractional diffusion-wave equationen_US
dc.subjectQuadratic B-Splineen_US
dc.subjectLinear B-Splineen_US
dc.titleSOLVING FRACTIONAL DIFFUSION AND FRACTIONAL DIFFUSION-WAVE EQUATIONS BY PETROV-GALERKIN FINITE ELEMENT METHODen_US
dc.typeArticleen_US

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