  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.
