Abstract
First, our work is to transform the space-time fractional approximate long water wave equations into nonlinear ordinary differential equations via the traveling wave transformation in the sense of conformable fractional derivative. Second, we simplify the nonlinear ordinary differential equations into an ordinary differential equation with only one variable by integration and some transformations. Finally, we can further get all single traveling wave solutions of the space-time fractional approximate long water wave equations by the complete discrimination system for the four-order polynomial method; these solutions include the hyperbolic function solutions, rational function solutions, and implicit solutions.
Highlights
E work of this study is as follows. In Section 2, we give the construction steps of traveling wave solutions for fractional partial differential equations
Where P is a polynomial of U and its derivatives
Q is a polynomial of U, the derivative of U and the derivative of V
Summary
E work of this study is as follows. In Section 2, we give the construction steps of traveling wave solutions for fractional partial differential equations. 1. Introduction e exact traveling wave solutions of fractional partial differential equations have attracted much attention from mathematicians and engineering experts [1–10]. The classification of all single traveling wave solutions of fractional partial differential equations can be constructed. We consider the space-time fractional approximate long water wave equations [17]:
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