A Variety of Novel Exact Solutions for Different Models With the Conformable Derivative in Shallow Water

Abstract

For different nonlinear time-conformable derivative models, a versatile built-in gadget, namely the generalized exp(−φ(ξ))-expansion (GEE) method, is devoted to retrieving different categories of new explicit solutions. These models include the time-fractional approximate long-wave equations, the time-fractional variant-Boussinesq equations, and the time-fractional Wu-Zhang system of equations. The GEE technique is investigated with the help of fractional complex transform and conformable derivative. As a result, we found four types of exact solutions involving hyperbolic function, periodic function, rational functional, and exponential function solutions. The physical significance of the explored solutions depends on the choice of arbitrary parameter values. Finally, we conclude that the GEE method is more effective in establishing the explicit new exact solutions than the exp(−φ(ξ))-expansion method.