Numerical and exact solutions for time fractional Burgers' equation

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dc.contributor.authorYokus, Asif
dc.contributor.authorKaya, Doğan
dc.date.accessioned2020-11-21T15:55:54Z
dc.date.available2020-11-21T15:55:54Z
dc.date.issued2017en_US
dc.departmentİstanbul Ticaret Üniversitesien_US
dc.description.abstractThe main purpose of this paper is to find an exact solution of the traveling wave equation of a nonlinear time fractional Burgers' equation using the expansion method and the Cole-Hopf transformation. For this purpose, a nonlinear time fractional Burgers' equation with the initial conditions considered. The finite difference method (FDM for short) which is based on the Caputo formula is used and some fractional differentials are introduced. The Burgers' equation is linearized by using the Cole-Hopf transformation for a stability of the FDM. It shows that the FDM is stable for the usage of the Fourier-Von Neumann technique. Accuracy of the method is analyzed in terms of the errors in L-2 and L-infinity. All of obtained results are discussed with an example of the Burgers' equation including numerical solutions for different situations of the fractional order and the behavior of potentials u is investigated with graphically. All the obtained numerical results in this study are presented in tables. We used the Mathematica software package in performing this numerical study. (C) 2017 All rights reserved.en_US
dc.identifier.doi10.22436/jnsa.010.07.06en_US
dc.identifier.endpage3428en_US
dc.identifier.issn2008-1898
dc.identifier.issn2008-1901
dc.identifier.issue7en_US
dc.identifier.startpage3419en_US
dc.identifier.urihttps://doi.org/10.22436/jnsa.010.07.06
dc.identifier.urihttps://hdl.handle.net/11467/4065
dc.identifier.volume10en_US
dc.identifier.wosWOS:000409101400006en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.language.isoenen_US
dc.publisherInt Scientific Research Publicationsen_US
dc.relation.ispartofJournal of Nonlinear Sciences and Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectNonlinear time fractional Burgers' equationen_US
dc.subjectan expansion methoden_US
dc.subjectfinite difference methoden_US
dc.subjectCaputo formulaen_US
dc.subjectlinear stabilityen_US
dc.subjectCole-Hopf transformationen_US
dc.titleNumerical and exact solutions for time fractional Burgers' equationen_US
dc.typeArticleen_US

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