In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the B...In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the Boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new （G＇/G）-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.展开更多
In this paper, the (G′/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation,...In this paper, the (G′/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established.展开更多
In the present article, He＇s fractional derivative, the ansatz method, the （ C / G）-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomts...In the present article, He＇s fractional derivative, the ansatz method, the （ C / G）-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomtsev-Petviashvili- Benjamin-Bona Mahony （KP-BBM）. As a result, different types of exact solutions are obtained. Also we have examined the relation between the solutions obtained from the different methods. These methods are an efficient mathematical tool for solving fractional differential equations （FDEs） and it can be applied to other nonlinear FDEs.展开更多
In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presen...In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.展开更多
In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is prop...In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie＇s modified Riemann-Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.展开更多
文摘In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the Boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new （G＇/G）-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.
文摘In this paper, the (G′/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established.
文摘In the present article, He＇s fractional derivative, the ansatz method, the （ C / G）-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomtsev-Petviashvili- Benjamin-Bona Mahony （KP-BBM）. As a result, different types of exact solutions are obtained. Also we have examined the relation between the solutions obtained from the different methods. These methods are an efficient mathematical tool for solving fractional differential equations （FDEs） and it can be applied to other nonlinear FDEs.
基金supported by the research grant under the Government of Malaysia
文摘In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.
基金supported by National Natural Science Foundation of China(No.11371267 and 11571245)Basic Project of Sichuan Provincial Science and Technology Department(No.2016JY0204)~~
文摘In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie＇s modified Riemann-Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.
