期刊
AIMS MATHEMATICS
卷 7, 期 7, 页码 12483-12513出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2022693
关键词
Caputo-Fabrizio and Atangana-Baleanu operators; fractional approximate long wave equations; fractional modified Boussinesq equations; Adomian decomposition method; natural transform
资金
- Deanship of Scientific Research at Umm Al-Qura University [22UQU4310396DSR07]
In this paper, the Natural decomposition approach and nonsingular kernel derivatives were used to explore the modified Boussinesq and approximate long wave equations. Convergence analysis, error analysis, and verification of the approach were performed. The results show that the suggested scheme is computationally accurate and effective in solving fractional coupled nonlinear complicated phenomena.
In this paper, we used the Natural decomposition approach with nonsingular kernel derivatives to explore the modified Boussinesq and approximate long wave equations. These equations are crucial in defining the features of shallow water waves using a specific dispersion relationship. In this research, the convergence analysis and error analysis have been provided. The fractional derivatives Atangana-Baleanu and Caputo-Fabrizio are utilised throughout the paper. To obtain the equations results, we used Natural transform on fractional-order modified Boussinesq and approximate long wave equations, followed by inverse Natural transform. To verify the approach, we focused on two systems and compared them to the exact solutions. We compare exact and analytical results with the use of graphs and tables, which are in strong agreement with each other, to demonstrate the effectiveness of the suggested approaches. Also compared are the results achieved by implementing the suggested approaches at various fractional orders, confirming that the result comes closer to the exact solution as the value moves from fractional to integer order. The numerical and graphical results show that the suggested scheme is computationally very accurate and simple to investigate and solve fractional coupled nonlinear complicated phenomena that exist in science and technology.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据