Department of Mathematics and Statistics, Sub-Campus Depalpur, University of Agriculture Faisalabad, Faisalabad, Pakistan.
Department of Mathematics and Statistics, University of Agriculture Faisalabad, Faisalabad, Pakistan.
PLoS One. 2024 May 28;19(5):e0303426. doi: 10.1371/journal.pone.0303426. eCollection 2024.
This paper aims to extend the applications of the projected fractional improved Adomian Decomposition method (fIADM) to the fractional order new coupled Korteweg-de Vries (cKdV) system. This technique is significantly recognized for its effectiveness in addressing nonlinearities and iteratively handling fractional derivatives. The approximate solutions of the fractional-order new cKdV system are obtained by employing the improved ADM in fractional form. These solutions play a crucial role in designing and optimizing systems in engineering applications where accurate modeling of wave phenomena is essential, including fluid dynamics, plasma physics, nonlinear optics, and other mathematical physics domains. The fractional order new cKdV system, integrating fractional calculus, enhances accuracy in modeling wave interactions compared to the classical cKdV system. Comparison with exact solutions demonstrates the high accuracy and ease of application of the projected method. This proposed technique proves influential in resolving fractional coupled systems encountered in various fields, including engineering and physics. Numerical results obtained using Mathematica software further verify and demonstrate its efficacy.
本文旨在将投影分数改进 Adomian 分解方法（fIADM）应用于分数阶新耦合 Korteweg-de Vries（cKdV）系统。该技术因其在处理非线性和迭代处理分数导数方面的有效性而得到广泛认可。通过采用改进的分数形式的 ADM，得到分数阶新 cKdV 系统的近似解。这些解在工程应用中设计和优化系统中起着至关重要的作用，这些系统需要准确地建模波现象，包括流体动力学、等离子体物理、非线性光学和其他数学物理领域。与经典 cKdV 系统相比，集成分数微积分的分数阶新 cKdV 系统增强了对波相互作用的建模准确性。与精确解的比较证明了所提出方法的高精度和易用性。该方法在解决各种领域（包括工程和物理）中遇到的分数阶耦合系统方面具有影响力。使用 Mathematica 软件获得的数值结果进一步验证并证明了其有效性。
