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On the solutions of nonlinear fractional Klein-Gordon equation with modified Riemann-Liouville derivative

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Özet

In this paper, fractional variational iteration method (FVIM) is applied for finding approximate analytical solutions of nonlinear fractional Klein-Gordon equation. Time-fractional derivative is described in the Riemann-Liouville sense. A new application of fractional variational iteration method (FVIM) is extended to derive analytical solutions in the form of a series for this equation. The behavior of the solutions and the effects of different values of fractional order α are indicated graphically. It is shown that the solutions obtained by the FVIM are reliable, convenient and effective for strongly nonlinear partial equations with modified Riemann-Liouville derivative.

Anahtar Kelimeler

Fractional Klein-Gordon equationFractional variational iteration methodRiemann-Liouville derivative
RDL Kalıcı Bağlantı (PID)
https://rdlopen.rawdatalibrary.net/r/gumushane/15783Resmi atıflarda kullanılan kalıcı adres
DOI
https://doi.org/10.1016/j.amc.2014.06.013Yayıncı resmi DOI adresi
Tam Kayıt
AlanDeğerDil
dc.contributor.authorMerdan, Mehmet
dc.date.accessioned2026-10-22T10:24:32.081704778Z
dc.date.available2026-10-22T10:24:32.081704778Z
dc.date.issued2014
dc.description.abstractIn this paper, fractional variational iteration method (FVIM) is applied for finding approximate analytical solutions of nonlinear fractional Klein-Gordon equation. Time-fractional derivative is described in the Riemann-Liouville sense. A new application of fractional variational iteration method (FVIM) is extended to derive analytical solutions in the form of a series for this equation. The behavior of the solutions and the effects of different values of fractional order α are indicated graphically. It is shown that the solutions obtained by the FVIM are reliable, convenient and effective for strongly nonlinear partial equations with modified Riemann-Liouville derivative.
dc.identifier.doi10.1016/j.amc.2014.06.013
dc.identifier.eissn1873-5649
dc.identifier.endpage888
dc.identifier.issn0096-3003
dc.identifier.scopus2-s2.0-84904569363
dc.identifier.startpage877
dc.identifier.urihttps://rdlopen.rawdatalibrary.net/r/gumushane/15783
dc.identifier.volume242
dc.identifier.wosWOS:000340563000079
dc.language.isoen
dc.publisherElsevier Inc.
dc.relation.ispartofApplied Mathematics and Computation
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectFractional Klein-Gordon equation
dc.subjectFractional variational iteration method
dc.subjectRiemann-Liouville derivative
dc.subject.classificationMathematics, Applied
dc.subject.classificationMathematics
dc.subject.otherEquations of motion
dc.subject.otherIterative methods
dc.subject.otherNonlinear equations
dc.subject.otherApproximate analytical solutions
dc.subject.otherFractional derivatives
dc.subject.otherKlein-Gordon equation
dc.subject.otherModified Riemann-Liouville derivative
dc.subject.otherRiemann-Liouville derivatives
dc.subject.otherRiemann-Liouville sense
dc.subject.otherStrongly nonlinear
dc.subject.otherVariational iteration method
dc.subject.otherLiouville equation
dc.titleOn the solutions of nonlinear fractional Klein-Gordon equation with modified Riemann-Liouville derivative
dc.typeReview Article
dspace.entity.typePublication
rdl.citation.scopus11
rdl.citation.wos11
rdl.oa.statusclosed
rdl.source.indexSCOPUS
rdl.source.indexWOS
rdl.wos.indexScience Citation Index Expanded (SCI-EXPANDED)