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

Amit Prakash1, Vijay Verma1, Dumitru Baleanu2,3
1Department of Mathematics, National Institute of Technology, Kurukshetra, India
2Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Etimesgut, Turkey
3Institute of Space Sciences, Magurele-Bucharest, Romania

Tóm tắt

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, $${L}_{2}$$ error norm and $${L}_{\infty }$$ error norm with q-HASTM and HPSTM.

Tài liệu tham khảo

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