Nonlinear analysis of a nonlinear modified KdV equation under Atangana Baleanu Caputo derivative

Basit Öğe Kaydı
dc.authoridAhmad, Shabir/0000-0002-5610-6248
dc.authoridUllah, Aman/0000-0003-4021-3599
dc.contributor.authorGulalai
dc.contributor.authorAhmad, Shabir
dc.contributor.authorRihan, Fathalla Ali
dc.contributor.authorUllah, Aman
dc.contributor.authorAl-Mdallal, Qasem M.
dc.contributor.authorAkgul, Ali
dc.date.accessioned2024-12-24T19:34:00Z
dc.date.available2024-12-24T19:34:00Z
dc.date.issued2022
dc.departmentSiirt Üniversitesi
dc.description.abstractThe focus of the current manuscript is to provide a theoretical and computational analysis of the new nonlinear time-fractional (2+1)-dimensional modified KdV equation involving the Atangana-Baleanu Caputo (ABC) derivative. A systematic and convergent technique known as the Laplace Adomian decomposition method (LADM) is applied to extract a semi-analytical solution for the considered equation. The notion of fixed point theory is used for the derivation of the results related to the existence of at least one and unique solution of the mKdV equation involving under ABC-derivative. The theorems of fixed point theory are also used to derive results regarding to the convergence and Picard's X-stability of the proposed computational method. A proper investigation is conducted through graphical representation of the achieved solution to determine that the ABC operator produces better dynamics of the obtained analytic soliton solution. Finally, 2D and 3D graphs are used to compare the exact solution and approximate solution. Also, a comparison between the exact solution, solution under Caputo-Fabrizio, and solution under the ABC operator of the proposed equation is provided through graphs, which reflect that ABC-operator produces better dynamics of the proposed equation than the Caputo-Fabrizio one.
dc.description.sponsorshipUnited Arab Emirates University, Al Ain, UAE [12S005-UPAR 2020]
dc.description.sponsorshipThe authors wish to express their sincere thanks to the honorable referees for their valuable comments and suggestions to improve the quality of the paper. In addition, authors would like to express their gratitude to the United Arab Emirates University, Al Ain, UAE for providing the financial support with Grant No. 12S005-UPAR 2020.
dc.identifier.doi10.3934/math.2022439
dc.identifier.endpage7865
dc.identifier.issn2473-6988
dc.identifier.issue5
dc.identifier.scopus2-s2.0-85124756702
dc.identifier.scopusqualityQ1
dc.identifier.startpage7847
dc.identifier.urihttps://doi.org/10.3934/math.2022439
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8380
dc.identifier.volume7
dc.identifier.wosWOS:000758376900019
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherAmer Inst Mathematical Sciences-Aims
dc.relation.ispartofAims Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectAtangana-Baleanu fractional operator
dc.subjectfixed point theory
dc.subjectLaplace Adomian decomposition
dc.titleNonlinear analysis of a nonlinear modified KdV equation under Atangana Baleanu Caputo derivative
dc.typeArticle

Dosyalar

Koleksiyon

WOS İndeksli Yayınlar Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu