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：本文基于再生核方法求解时间分数阶Vakhnenko-Parkes方程。该技术的主要工具包括再生核理论、标准正交基、若干重要Hilbert空间、约束齐次化以及正交化过程。再生核方法的主要优势在于其真正无网格特性。通过将再生核Hilbert空间方法应用于时间分数阶Vakhnenko-Parkes方程，所得解以级数形式呈现。获得的解唯一收敛至精确解。研究表明，所实施的方法具有高度有效性。通过表格与图表展示了再生核Hilbert空间方法的有效性，并采用不同误差范数及误差收敛阶验证了该方法的完备性。