New Exact Solutions of the Time-Fractional Nonlinear Dispersive KdV Equation

Abstract

In this study, new version of the extended trial equation method is applied the nonlinear fractional partial differential equations. The fractional partial differential equations can be turned into the nonlinear non-fractional ordinary differential equations by the fractional derivative and traveling wave transformation. So, we find some traveling wave solutions to the time-fractional nonlinear dispersive KdV equation by the using of the complete discrimination system for polynomial method. As a result, these exact solutions to this nonlinear problem are constructed such as single king solution and hyperbolic function solutions.