This article is concerned with solving the time fractional Vakhnenko Parkes equation using the reproducing kernels. Reproducing kernel theory, the normal basis, some important Hilbert spaces, homogenization of constraints, and the orthogonalization process are the main tools of this technique. The main advantage of reproducing kernel method is it is truly meshless. The solutions obtained by the implementation reproducing kernels Hilbert space method on the time-fractional Vakhnenko Parkes equation is in the form of a series. The obtained solution converges to the exact solution uniquely. It is observed that the implemented method is highly effective. The effectiveness of reproducing kernel Hilbert space method is presented through the tables and graphs. The perfectness of this method is tested by taking different error norms and the order of convergence of the errors.

翻译：本文关注利用再生核方法求解时间分数阶Vakhnenko Parkes方程。再生核理论、规范正交基、若干重要希尔伯特空间、约束齐次化及正交化过程是该技术的核心工具。再生核方法的主要优势在于其完全无网格特性。通过将再生核希尔伯特空间方法应用于时间分数阶Vakhnenko Parkes方程，所得解呈现级数形式。所获解能唯一收敛于精确解。研究表明该方法具有显著有效性。通过数据表格与曲线图展示了再生核希尔伯特空间方法的效能。通过采用不同误差范数及误差收敛阶数验证了该方法的完备性。