New exact solitary wave solutions to the space-time fractional differential equations with conformable derivative

Abstract

The exact wave solutions to the space-time fractional modified Benjamin-Bona-Mahony (mBBM) and space time fractional Zakharov-Kuznetsov Benjamin-Bona-Mahony (ZKBBM) equations are studied in the sense of conformable derivative. The existence of chain rule and the derivative of composite functions permit the nonlinear fractional differential equations (NLFDEs) to convert into the ordinary differential equation using wave transformation. The wave solutions of these equations are examined by means of the expanding and effective two variable (G'/G, 1/G)-expansion method. The solutions are obtained in the form of hyperbolic, trigonometric and rational functions containing parameters. The method is efficient, convenient, accessible and is the generalization of the original (G'/G)-expansion method.