New analytical and approximate solutions for the time-conformable fractional Kersten–Krasil’shchik coupled KdV–mKdV nonlinear system

Purpose We present novel analytical and numerical solutions using a unified technique and conformable residual power series approach for the conformable fractional Kersten–Krasil’shchik coupled KdV–mKdV nonlinear system. Design/methodology/approach We employ the conformable residual power series method for obtaining new analytical and numerical solutions of the time-fractional Kersten–Krasil’shchik coupled KdV–mKdV nonlinear system. We conduct a comprehensive comparison between the exact solutions obtained and their numerical counterparts. Findings Our analysis, presented through tabular and graphical representations, showcases the efficacy and reliability of the conformable residual power series method in tackling nonlinear models emerging in different fields of science and engineering. We compare our results with those obtained using other methods and exact solutions. The comparison demonstrates that the proposed method is efficient, accurate and provides significant and reliable solutions. Originality/value For the first time, we employ the conformable residual power series method for obtaining new analytical and numerical solutions of the time-fractional Kersten–Krasil’shchik coupled KdV–mKdV nonlinear system.