New generalized (G’/G)-expansion method for solving (3+1)-dimensional conformable time fractional KdV-ZK equation

Abstract

In this study, the new generalized (G'/G)-expansion method is employed to extract abundant new travelling wave solutions in terms of trigonometric functions, hyperbolic functions and rational forms. This method provides some wide-ranging solutions from which some existing solutions for specific values of integral constants will be re-established and some new solutions will be found. The method is applied to the (3+1)-dimensional Kdv- Zakharov-Kuznetsov (KdV-ZK) equation with time fractional derivative. The fractional derivative is described in the sense of conformable fractional derivative (CFD). The CFD is new simple well-behaved definition that can convert the fractional derivative into ordinary derivative. The obtained solutions show that the introduced method with the CFD is reliable and efficient technique for the (3+1)-dimensional time fractional KdV-ZK equation.