This article is concerned with an approximate analytical solution for the time fractional Kudryashov Sinelshchikov equation by using the reproducing kernel Hilbert space method. The main tools of this method are reproducing kernel theory, some important Hilbert spaces, the normal basis, orthogonalisation process, and homogenization. The effectiveness of reproduc ing kernel Hilbert space method is presented through the tables and graphs. These computa tional results indicate that this method is highly accurate and efficient for the time fractional Kudryashov Sinelshchikov equation. Also, it is demonstrated that the approximate solution uniformly converges to exact solution by using reproducing kernel Hilbert space method.

翻译：本文利用再生核希尔伯特空间方法研究时间分数阶Kudryashov Sinelshchikov方程的近似解析解。该方法的主要工具包括再生核理论、若干重要希尔伯特空间、规范基、正交化过程以及均匀化。通过数据表和曲线图展示了再生核希尔伯特空间方法的有效性。计算结果表明，该方法对于时间分数阶Kudryashov Sinelshchikov方程具有高精度与高效率。同时证明，采用再生核希尔伯特空间方法获得的近似解一致收敛于精确解。