Nonlinear regularized long-wave models with a new integral transformation applied to the fractional derivative with power and Mittag-Leffler kernel

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dc.contributor.authorYavuz, Mehmet
dc.contributor.authorAbdeljawad, Thabet
dc.date.accessioned2024-02-23T14:29:08Z
dc.date.available2024-02-23T14:29:08Z
dc.date.issued2020
dc.departmentNEÜen_US
dc.description.abstractThis paper presents a fundamental solution method for nonlinear fractional regularized long-wave (RLW) models. Since analytical methods cannot be applied easily to solve such models, numerical or semianalytical methods have been extensively considered in the literature. In this paper, we suggest a solution method that is coupled with a kind of integral transformation, namely Elzaki transform (ET), and apply it to two different nonlinear regularized long wave equations. They play an important role to describe the propagation of unilateral weakly nonlinear and weakly distributer liquid waves. Therefore, these equations have been noticed by scientists who study waves their movements. Particularly, they have been used to model a large class of physical and engineering phenomena. In this context, this paper takes into consideration an up-to-date method and fractional operators, and aims to obtain satisfactory approximate solutions to nonlinear problems. We present this achievement, firstly, by defining the Elzaki transforms of Atangana-Baleanu fractional derivative (ABFD) and Caputo fractional derivative (CFD) and then applying them to the RLW equations. Finally, numerical outcomes giving us better approximations after only a few iterations can be easily obtained.en_US
dc.description.sponsorshipTUBITAK (The Scientific and Technological Research Council of Turkey); Prince Sultan University [RG-DES-2017-01-17]en_US
dc.description.sponsorshipMehmet Yavuz was supported by TUBITAK (The Scientific and Technological Research Council of Turkey). The author Thabet Abdeljawad would like to thank Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17.en_US
dc.identifier.doi10.1186/s13662-020-02828-1
dc.identifier.issn1687-1847
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-85088017526en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.1186/s13662-020-02828-1
dc.identifier.urihttps://hdl.handle.net/20.500.12452/14556
dc.identifier.volume2020en_US
dc.identifier.wosWOS:000552400000003en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofAdvances In Difference Equationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectAtangana-Baleanu Fractional Derivativeen_US
dc.subjectCaputo Fractional Derivativeen_US
dc.subjectApproximate-Analytical Solutionen_US
dc.subjectNonlinear Regularized Long Wave Modelen_US
dc.subjectElzaki Transformen_US
dc.titleNonlinear regularized long-wave models with a new integral transformation applied to the fractional derivative with power and Mittag-Leffler kernelen_US
dc.typeArticleen_US

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