Homotopy analysis method for space- and time-fractional KdV equation

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dc.contributor.authorMohyud-Din, Syed Tauseef
dc.contributor.authorYildirim, Ahmet
dc.contributor.authorYuluklu, Eda
dc.date.accessioned2019-10-27T21:33:52Z
dc.date.available2019-10-27T21:33:52Z
dc.date.issued2012
dc.departmentEge Üniversitesien_US
dc.description.abstractPurpose - The purpose of this paper is to present numerical solutions for the space- and time-fractional Korteweg-de Vries (KdV) equation using homotopy analysis method (HAM). The space and time-fractional derivatives are described in the Caputo sense. The paper witnesses the extension of HAM for fractional KdV equations. Design/methodology/approach - This paper presents numerical solutions for the space- and time-fractional KdV equation using HAM. The space and time-fractional derivatives are described in the Caputo sense. Findings - In this paper, the application of homotopy analysis method was extended to obtain explicit and numerical solutions of the time- and space-fractional KdV equation with initial conditions. The homotopy analysis method was clearly a very efficient and powerful technique in finding the solutions of the proposed equations. Originality/value - In this paper, the application of HAM was extended to obtain explicit and numerical solutions of the time- and space-fractional KdV equation with initial conditions. The HAM was clearly very efficient and powerful technique in finding the solutions of the proposed equations. The obtained results demonstrate the reliability of the algorithm and its wider applicability to fractional nonlinear evolution equations. Finally, the recent appearance of nonlinear fractional differential equations as models in some fields such as the thermal diffusion in fractal media makes it necessary to investigate the method of solutions for such equations and the authors hope that this paper is a step in this direction.en_US
dc.identifier.doi10.1108/09615531211255798
dc.identifier.endpage941en_US
dc.identifier.issn0961-5539
dc.identifier.issn0961-5539en_US
dc.identifier.issue06.Julen_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.startpage928en_US
dc.identifier.urihttps://doi.org/10.1108/09615531211255798
dc.identifier.urihttps://hdl.handle.net/11454/45450
dc.identifier.volume22en_US
dc.identifier.wosWOS:000310411700015en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherEmerald Group Publishing Limiteden_US
dc.relation.ispartofInternational Journal of Numerical Methods For Heat & Fluid Flowen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectTopologyen_US
dc.subjectCalculusen_US
dc.subjectMathematical modellingen_US
dc.subjectHomotopy analysis methoden_US
dc.subjectFractional calculusen_US
dc.titleHomotopy analysis method for space- and time-fractional KdV equationen_US
dc.typeArticleen_US

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