In this article, the space-time fractional Benjamin-Bona-Mahoney equation is investigated via applying the first kind of elliptic equation method. As a result, based on the Backlund transformations and some seed solut...In this article, the space-time fractional Benjamin-Bona-Mahoney equation is investigated via applying the first kind of elliptic equation method. As a result, based on the Backlund transformations and some seed solutions of the first kind of elliptic equation, families of infinite sequence solutions are presented. This approach is also applicable to many other nonlinear fractional differential equations.展开更多
In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified...In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona- Mahoney （mBBM） equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions： amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional deriva- tives are described in the modified Riemann-Liouville sense.展开更多
基金Scientific Research Program Funded by Shaanxi Provincial Education Department(No.2013JK0572,ZK0953)Natural Science Basic Research Plan in Shaanxi Province of China(No.2014JM1027)
文摘In this article, the space-time fractional Benjamin-Bona-Mahoney equation is investigated via applying the first kind of elliptic equation method. As a result, based on the Backlund transformations and some seed solutions of the first kind of elliptic equation, families of infinite sequence solutions are presented. This approach is also applicable to many other nonlinear fractional differential equations.
文摘In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona- Mahoney （mBBM） equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions： amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional deriva- tives are described in the modified Riemann-Liouville sense.
