Traveling wave solutions of generalized seventh- order time-fractional KdV models through He-Laplace algorithm
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Tarih
2023
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Non-linear evolution equations play a prominent role in describing a wide range of phe-nomena in optical fibers, fluid dynamics, electromagnetic radiation, plasma and solid state physics. An important category of non-linear evolution models that characterizes shallow wave phenomena are the Korteweg-de Vries (KdV) models. In this regard, time-fractional Korteweg-de Vries models of seventh order are the main focus of this research. A general KdV seventh-order equation is con-sidered with different coefficients to form Lax, Kaup-Kuperschimdt and Sawada-Kotera-Ito KdV models. An efficient semi-analytical algorithm named as He-Laplace (HLM) is applied for the solu-tion of these models. In this algorithm, Laplace transform is hybrid with homotopy perturbation method (HPM). This study provides important results as non-linear evolution seventh-order models in fractional sense have not been captured through HLM in current literature. Absolute errors are computed and compared with already existing results to confirm the superiority of proposed algo-rithm over other existing techniques. Numerical and graphical investigations are conducted to eval-uate the approximate series form solutions. The dynamic behavior of fractional parameter is observed by calculating residual errors and plotting two dimensional diagrams throughout the fractional-domain. Analysis confirms that the proposed methodology provides an effective and con-venient way for solving fractional KdV models. (c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Açıklama
Anahtar Kelimeler
Seventh order Korteweg-de Vries models, Time-fractional Lax model, Time-fractional Kaup-Kupershmidt model, Time-fractional Sawada- Kotera-Ito model, He-Laplace
Kaynak
Alexandria Engineering Journal
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
70
