Two Novel Methods for Fractional Nonlinear Whitham–Broer–Kaup Equations Arising in Shallow Water

Abstract

In the present paper, we investigate the approximate analytic solution of the time-fractional nonlinear coupled Whitham–Broer–Kaup equations arising in shallow water with the aid of two novel approaches namely q -homotopy analysis Sumudu transform method (q-HASTM) and Homotopy perturbation Sumudu transform method (HPSTM). Uniqueness and convergence analysis of the coupled WBK equations via q-HASTM are accessible. We applied the suggested techniques to a pair of examples, plotted the results and analyse the error, L2 error norm and L∞ error norm with q-HASTM and HPSTM.