Utilizing the Optimal Auxiliary Function Method for the Approximation of a Nonlinear Long Wave System considering Caputo Fractional Order

IF 1.7 4区 工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Complexity Pub Date : 2024-05-20 DOI:10.1155/2024/8357221
Aaqib Iqbal, Rashid Nawaz, Hina Hina, Abdulaziz Garba Ahmad, Homan Emadifar
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引用次数: 0

Abstract

In this article, we explore the utilization of the Caputo derivative and the Riemann–Liouville (R–L) fractional integral to analyze the optimal auxiliary function method for approximating fractional nonlinear long waves. Approximate long wave equation with a distinct dispersion relation offers the most accurate description of shallow water wave properties. Various methods, including the Adomian decomposition technique, the variational iteration method, the optimum homotopy asymptotic method, and the new iterative technique, have been employed and compared to those obtained using the fractional-order approximate long wave equation. The results of our study indicate that the optimal auxiliary function method is highly successful and practically simple, achieving better and more rapid convergence after just one repetition. This method is recognized as an efficient approach, demonstrating high precision in solving intriguing and intricate problems. Furthermore, it proves to be more time and resource efficient than other relevant analytical techniques, leading to significant savings in both volume and time. Compared to the Adomian decomposition technique, the new iterative technique, the variational iteration method, and the optimum homotopy asymptotic method, the suggested technique is extremely accurate computationally. It is also easy to analyze and solve fractionally linked nonlinear complex phenomena that arise in science and technology. We present the numerical and graphical findings that support these conclusions.

Abstract Image

利用最优辅助函数法近似考虑卡普托分数阶的非线性长波系统
本文探讨了如何利用卡普托导数和黎曼-刘维尔(R-L)分数积分来分析近似分数非线性长波的最佳辅助函数方法。具有明显频散关系的近似长波方程能最准确地描述浅水波浪特性。我们采用了多种方法,包括 Adomian 分解技术、变异迭代法、最优同调渐近法和新迭代技术,并与使用分数阶近似长波方程得到的结果进行了比较。我们的研究结果表明,最优辅助函数法非常成功,而且实际操作简单,只需重复一次就能实现更好、更快的收敛。这种方法被公认为是一种高效的方法,在解决复杂难题时表现出很高的精度。此外,与其他相关的分析技术相比,该方法被证明更节省时间和资源,从而大大节省了工作量和时间。与阿多米分解技术、新迭代技术、变异迭代法和最优同调渐近法相比,建议的技术在计算上极为精确。它还易于分析和解决科学技术中出现的分数联系非线性复杂现象。我们展示了支持这些结论的数值和图形结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Complexity
Complexity 综合性期刊-数学跨学科应用
CiteScore
5.80
自引率
4.30%
发文量
595
审稿时长
>12 weeks
期刊介绍: Complexity is a cross-disciplinary journal focusing on the rapidly expanding science of complex adaptive systems. The purpose of the journal is to advance the science of complexity. Articles may deal with such methodological themes as chaos, genetic algorithms, cellular automata, neural networks, and evolutionary game theory. Papers treating applications in any area of natural science or human endeavor are welcome, and especially encouraged are papers integrating conceptual themes and applications that cross traditional disciplinary boundaries. Complexity is not meant to serve as a forum for speculation and vague analogies between words like “chaos,” “self-organization,” and “emergence” that are often used in completely different ways in science and in daily life.
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