Fractional Transformation Method for Constructing Solitary Wave Solutions to Some Nonlinear Fractional Partial Differential Equations

The aim of this paper is twofold: First, we derive both the factional KdV hierarchy and the fractional Burger hierarchy. Second, a fractional transform is conducted to convert nonlinear fractional partial differential equations (PDEs) into classical PDEs. Then, solitary ansatze methods will be used to obtain solitary wave solutions to the reduced PDEs. This new transformation has been tested to three different models of nonlinear fractional differential equations; the time- and space-fractional mKdV, time- and space-fractional Burger equation and time-fractional nonlinear biological population equation.