Lie Analysis and Novel Analytical Solutions for the Time-Fractional Coupled Whitham–Broer–Kaup Equations

  • R. SadatEmail author
  • M. M. Kassem
Original Paper


The Lie point symmetries for the fractional Riemann–Liouville system are used to reduce Fractional Whitham–Broer–Kaup (FWBK) equations to nonlinear fractional ordinary differential equations using the prolongation theorem. FWBK describe the propagation of fluid with different dispersive coefficients in shallow waters. Through the conformable derivative, we apply the integrating factors and Riccati–Bernoulli sub-equation methods. New solutions have been generated. Comparison with previous works has been presented. A mathematical modeling for the long water wave motion between two non-mixed fluids was also studied.


Time fractional Whitham–Broer–Kaup equations Conformable derivatives Lie symmetry Riccati–Bernoulli (RB) sub-equation Integrating factors Explicit solutions 



We would thank the editing board and reviewers for their valuable response and fast reply that enhance the obtained results.


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© Springer Nature India Private Limited 2019

Authors and Affiliations

  1. 1.Faculty of Engineering, Physics and Mathematics DepartmentZagazig UniversityAsh SharqiyahEgypt

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