Recently, non-linear fractional partial differential equations are used to model many phenomena in applied sciences and engineering. In this study, the modified simple equation scheme is implemented to obtain some new traveling wave solutions of the non-linear conformable time-fractional approximate long water wave equation and the non-linear conformable coupled time-fractional Boussinesq-Burger equation, which are used in the expression of shallow-water waves. The time- fractional derivatives are described in terms of conformable fractional derivative sense. Consequently, new exact traveling wave solutions of both equations are achieved. The graphics and correctness of the wave solutions are obtained with the Mathematica package program.
In this study, some new exact wave solutions of nonlinear partial differential equations are investigated by the modified simple equation method. This method is applied to the (2 + 1)-dimensional Calogero-Bogoyavlenskii-Schiff equation and the (3 + 1)-dimensional Jimbo-Miwa equation. Our applications reveal how to use the proposed method to solve nonlinear partial differential equations with the balance number equal to two. Consequently, some new exact traveling wave solutions of these equations are achieved, and types of waves are determined. To verify our results and draw the graphs of the solutions, we use the Mathematica package program.
Recently, a new generalization of the double Laplace transform
and double Sumudu transform, namely, double Shehu transform, has been
introduced. This study has derived the double Shehu transform (DHT)
formulas for the fractional Caputo operators. We then applied this generalized integral transform to solve fractional partial differential equations
involving Caputo derivative.
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