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<p>The main aim of this paper is to obtain the approximate series solution of the time-fractional nonlinear Zakharov–Kuznetsov (TFZK) equations using the Laplace residual power series (LRPS) method. LRPS method is a coupling where Laplace transformation is gracefully combined with the residual power series method. One important feature of the LRPS technique is that it uses the concept of limits at infinity, which help us to determine the unknown coefficients of the convergent power series solution. Caputo fractional derivative is used in the formulation of Zakharov–Kuznetsov (ZK) equations. The ZK equations with time-fractional derivative have significant implications in the study of wave dynamics in ocean-based coastal regions, making their approximate solution essential for understanding complex wave phenomena. To validate the effectiveness of the LRPS approach, we analysed two different forms of the TFZK equation. Simultaneously, we visually captured the physical behaviour of the approximate solution using various tables and plots for different fractional orders. Numerical simulation is demonstrated using Maple and Matlab. Comparative analyses were performed with other existing methods, demonstrating the superiority of the LRPS method in solving TFZK equations.</p>

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Application of extended residual power series method for time-fractional Zakharov–Kuznetsov equations in ocean-based coastal wave

  • 期刊论文

  • 发表日期：

    2025年7月9日

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  • Sanjeev Yadav,
  • Ramesh Kumar Vats,
  • Anjali Rao

摘要

The main aim of this paper is to obtain the approximate series solution of the time-fractional nonlinear Zakharov–Kuznetsov (TFZK) equations using the Laplace residual power series (LRPS) method. LRPS method is a coupling where Laplace transformation is gracefully combined with the residual power series method. One important feature of the LRPS technique is that it uses the concept of limits at infinity, which help us to determine the unknown coefficients of the convergent power series solution. Caputo fractional derivative is used in the formulation of Zakharov–Kuznetsov (ZK) equations. The ZK equations with time-fractional derivative have significant implications in the study of wave dynamics in ocean-based coastal regions, making their approximate solution essential for understanding complex wave phenomena. To validate the effectiveness of the LRPS approach, we analysed two different forms of the TFZK equation. Simultaneously, we visually captured the physical behaviour of the approximate solution using various tables and plots for different fractional orders. Numerical simulation is demonstrated using Maple and Matlab. Comparative analyses were performed with other existing methods, demonstrating the superiority of the LRPS method in solving TFZK equations.