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Shallow Water Wave Models with and without Singular Kernel: Existence, Uniqueness, and Similarities
Joint Authors
Kumar, Sunil
Doungmo Goufo, Emile Franc
Source
Mathematical Problems in Engineering
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-02-06
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
After the recent introduction of the Caputo-Fabrizio derivative by authors of the same names, the question was raised about an eventual comparison with the old version, namely, the Caputo derivative.
Unlike Caputo derivative, the newly introduced Caputo-Fabrizio derivative has no singular kernel and the concern was about the real impact of this nonsingularity on real life nonlinear phenomena like those found in shallow water waves.
In this paper, a nonlinear Sawada-Kotera equation, suitable in describing the behavior of shallow water waves, is comprehensively analyzed with both types of derivative.
In the investigations, various fixed-point theories are exploited together with the concept of Piccard K-stability.
We are then able to obtain the existence and uniqueness results for the models with both versions of derivatives.
We conclude the analysis by performing some numerical approximations with both derivatives and graphical simulations being presented for some values of the derivative order γ.
Similar behaviors are pointed out and they concur with the expected multisoliton solutions well known for the Sawada-Kotera equation.
This great observation means either of both derivatives is suitable to describe the motion of shallow water waves.
American Psychological Association (APA)
Doungmo Goufo, Emile Franc& Kumar, Sunil. 2017. Shallow Water Wave Models with and without Singular Kernel: Existence, Uniqueness, and Similarities. Mathematical Problems in Engineering،Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1190447
Modern Language Association (MLA)
Doungmo Goufo, Emile Franc& Kumar, Sunil. Shallow Water Wave Models with and without Singular Kernel: Existence, Uniqueness, and Similarities. Mathematical Problems in Engineering No. 2017 (2017), pp.1-9.
https://search.emarefa.net/detail/BIM-1190447
American Medical Association (AMA)
Doungmo Goufo, Emile Franc& Kumar, Sunil. Shallow Water Wave Models with and without Singular Kernel: Existence, Uniqueness, and Similarities. Mathematical Problems in Engineering. 2017. Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1190447
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1190447