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

Abstract

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.