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The novel numerical solutions for time-fractional Fornberg-Whitham equation by using fractional natural transform decomposition method

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Bibliographic Details
Title: The novel numerical solutions for time-fractional Fornberg-Whitham equation by using fractional natural transform decomposition method
Authors: Aslı Alkan, Halil Anaç
Source: AIMS Mathematics, Vol 9, Iss 9, Pp 25333-25359 (2024)
Publisher Information: American Institute of Mathematical Sciences (AIMS), 2024.
Publication Year: 2024
Subject Terms: time-fractional partial differential equation, fractional natural transform decomposition method, mittag-leffler function, 0103 physical sciences, QA1-939, adomian polynomials, variational iteration method, 01 natural sciences, Mathematics
Description: The time-fractional partial differential equations were solved by the fractional natural transform decomposition method. Fractional derivatives are Caputo sense. The Fornberg-Whitham equation is a generalization of the Korteweg-de Vries (KdV) equation, which describes the propagation of long waves in shallow water. It includes higher-order dispersion terms, making it applicable to a wider range of dispersive media the fractional natural transform decomposition method (FNTDM) was also used to examine applications, and the solutions obtained by this method have been compared to those obtained by the variational iteration method, fractional variational iteration method, and homotopy perturbation method. In addition, the MAPLE package drew graphs of the solutions of nonlinear time-fractional partial differential equations, taking into account physics. The method described in this study exhibited a notable degree of computational precision and straightforwardness when used to the analysis and resolution of intricate phenomena pertaining to fractional nonlinear partial differential equations within the domains of science and technology.
Document Type: Article
ISSN: 2473-6988
DOI: 10.3934/math.20241237
Access URL: https://doaj.org/article/0d9900bf4a0b45c49fdb9aab1cdec01d
Accession Number: edsair.doi.dedup.....457ee34f20cb5809a70412d6b8248ab7
Database: OpenAIRE
Description
Abstract:The time-fractional partial differential equations were solved by the fractional natural transform decomposition method. Fractional derivatives are Caputo sense. The Fornberg-Whitham equation is a generalization of the Korteweg-de Vries (KdV) equation, which describes the propagation of long waves in shallow water. It includes higher-order dispersion terms, making it applicable to a wider range of dispersive media the fractional natural transform decomposition method (FNTDM) was also used to examine applications, and the solutions obtained by this method have been compared to those obtained by the variational iteration method, fractional variational iteration method, and homotopy perturbation method. In addition, the MAPLE package drew graphs of the solutions of nonlinear time-fractional partial differential equations, taking into account physics. The method described in this study exhibited a notable degree of computational precision and straightforwardness when used to the analysis and resolution of intricate phenomena pertaining to fractional nonlinear partial differential equations within the domains of science and technology.
ISSN:24736988
DOI:10.3934/math.20241237