分形分数阶导数下非线性Boussinesq方程的理论与数值分析

IF 2.4 Q2 ENGINEERING, MECHANICAL Nonlinear Engineering - Modeling and Application Pub Date : 2023-01-01 DOI:10.1515/nleng-2022-0338
Obaid J. Algahtani
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引用次数: 0

摘要

研究了分形分数阶Caputo导数下的非线性Boussinesq方程。一般级数解是用带分解的二重拉普拉斯变换计算的。在Caputo分形分数阶导数下,研究了模型的收敛性和稳定性。对于所得解的数值说明,考虑了具体的算例和合适的初始条件。通过考虑时间(t) \左(t)的小值,得到分形分数阶导数下的单孤波解。波的传播具有对称的形式。孤波的振幅会随着时间的推移而减弱,它长长的尾巴会延伸很长一段距离。结果表明,分形分数阶导数是研究非线性系统的一种极具建设性的工具。对紧凑性进行了误差分析。
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Theoretical and numerical analysis of nonlinear Boussinesq equation under fractal fractional derivative
Abstract A nonlinear Boussinesq equation under fractal fractional Caputo’s derivative is studied. The general series solution is calculated using the double Laplace transform with decomposition. The convergence and stability analyses of the model are investigated under Caputo’s fractal fractional derivative. For the numerical illustrations of the obtained solution, specific examples along with suitable initial conditions are considered. The single solitary wave solutions under fractal fractional derivative are attained by considering small values of time ( t ) \left(t) . The wave propagation has a symmetrical form. The solitary wave’s amplitude diminishes over time, and its extended tail expands over a long distance. It is observed that the fractal fractional derivatives are an extremely constructive tool for studying nonlinear systems. An error analysis is also carried out for compactness.
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来源期刊
CiteScore
6.20
自引率
3.60%
发文量
49
审稿时长
44 weeks
期刊介绍: The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.
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