Semi-Analytical Solutions of the Multi-Dimensional Time-Fractional Solitary Water Wave Equations Using RPS Method

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-12-30 DOI:10.1002/mma.10665

Rakesh Kumar Meena, Sushil Kumar

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引用次数: 0

Abstract

This article concerns the use of the residual power series (RPS) approach to get the semi-analytical solutions of multi-dimensional Korteweg-de Vries (KdV), that is, shallow water wave equations with any arbitrary time-fractional order ( $γ$ ). The time-fractional derivative is considered in the Caputo sense. The solutions of the fractional KdV equation obtained using the RPS method for $γ = 1$ are compared with the exact solutions of the integer-order KdV equation to show the RPS method's effectiveness, accuracy, and convergence. Some examples are also solved to study the effects of the fractional derivative $(γ)$ on the wave's amplitude.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.