In this paper, we establish exact solutions for some nonlinear fractional differential equations (FDEs). The first integral method with help of the fractional complex transform (FCT) is used to obtain exact solutions for the time fractional modified Korteweg–de Vries (fmKdV) equation and the space–time fractional modified Benjamin–Bona–Mahony (fmBBM) equation. This method is efficient and powerful in solving kind of other nonlinear FDEs.

No abstract

No abstract

The first integral method was used to construct exact solutions of the Zoomeron and Klein-Gordon-Zakharov equations. The obtained results include new soliton and periodic solutions. The work confirms the significant features of the employed method and shows the variety of the obtained solutions. Throughout the paper, all the calculations are made with the aid of the Maple packet program.

In this paper, the (G /G, 1/G) and (1/G )-expansion methods with the aid of Maple are used to obtain new exact traveling wave solutions of the Boussinesq equation and the system of variant Boussinesq equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. It is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering.