( $$\frac{G^{'}}{G^{2}}$$ G ′ G 2 )-Expansion method: new traveling wave solutions for some nonlinear fractional partial differential equations

Abstract

In this study, some new traveling wave solutions for fractional partial differential equations (PDEs) have been developed. The time-fractional Burgers equation, fractional biological population model and space-time fractional Whitham Broer Kaup equations have been considered. These equations have significant importance in different areas such as fluid mechanics, determination of birth and death rates and propagation of shallow water waves. The analytical technique ( $$\frac{G^{'}}{G^{2}}$$ ) has been utilized for finding the new traveling wave solutions of the considered fractional PDEs. ( $$\frac{G^{'}}{G^{2}}$$ )-expansion method is a very useful approach and exceptionally helpful as contrast with other analytical methods. The proposed method provides three unique sort of solutions such as hyperbolic, trigonometric and rational solutions. This approach is likewise applicable to other nonlinear fractional models.