共查询到20条相似文献,搜索用时 15 毫秒
1.
FENG Qing-Hua 《理论物理通讯》2014,62(2):167-172
In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space—time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. 相似文献
2.
Exact Solutions for Fractional Differential-Difference Equations by (G′/G)-Expansion Method with Modified Riemann-Liouville Derivative 下载免费PDF全文
Ahmet Bekir Ozkan Guner Burcu Ayhan & Adem C. Cevikel 《advances in applied mathematics and mechanics.》2016,8(2):293-305
In this paper, the ($G′/G$)-expansion method is suggested to establish new
exact solutions for fractional differential-difference equations in the sense of modified
Riemann–Liouville derivative. The fractional complex transform is proposed to convert
a fractional partial differential difference equation into its differential difference
equation of integer order. With the aid of symbolic computation, we choose nonlinear
lattice equations to illustrate the validity and advantages of the algorithm. It is shown
that the proposed algorithm is effective and can be used for many other nonlinear
lattice equations in mathematical physics and applied mathematics. 相似文献
3.
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(m BBM) equation, the time fractional m Kd V 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 derivatives are described in the modified Riemann–Liouville sense. 相似文献
4.
We introduce conformable fractional Nikiforov-Uvarov (NU) method by means of conformable fractional derivative which is the most natural definition in non-integer calculus. Since, NU method gives exact eigenstate solutions of Schrödinger equation (SE) for certain potentials in quantum mechanics, this method is carried into the domain of fractional calculus to obtain the solutions of fractional SE. In order to demonstrate the applicability of the conformable fractional NU method, we solve fractional SE for harmonic oscillator potential, Woods-Saxon potential, and Hulthen potential. 相似文献
5.
Qinghua Feng 《Chinese Journal of Physics (Taipei)》2018,56(6):2817-2828
In this paper, we present an approach for seeking exact solutions with coefficient function forms of conformable fractional partial differential equations. By a combination of an under-determined fractional transformation and the Jacobi elliptic equation, exact solutions with coefficient function forms can be obtained for fractional partial differential equations. The innovation point of the present approach lies in two aspects. One is the fractional transformation, which involve the traveling wave transformations used by many articles as special cases. The other is that more general exact solutions with coefficient function forms can be found, and traveling wave solutions with constants coefficients are only special cases of our results. As of applications, we apply this method to the space-time fractional (2+1)-dimensional dispersive long wave equations and the time fractional Bogoyavlenskii equations. As a result, some exact solutions with coefficient function forms for the two equations are successfully found. 相似文献
6.
无阻尼单摆运动微分方程是一种具有物理背景的非线性常微分方程,研究其精确解和解法是非线性科学中的一个重要内容.在F展开法的基础上,应用反正切分式变换正弦函数方法,并引入Riccati辅助方程,得到了4种无阻尼单摆方程精确解的结果.达到了丰富此类方程求解技巧和精确解的目的.总结得出此类方程应用反正切分式变换方法具有一定普适性的结论. 相似文献
7.
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. 相似文献
8.
In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie's modified Riemann–Liouville derivative. The efficiency and power of this approach are demonstrated by applying it successfully to some important fractional differential equations, namely, the time fractional Burgers, fractional Sawada–Kotera, and fractional coupled mKdV equation. A variety of new exact solutions to these equations under study are constructed. 相似文献
9.
Cheng-Shi Liu 《理论物理通讯》2020,72(5):55006-51
Finding exact solutions for Riemann–Liouville(RL) fractional equations is very difficult. We propose a general method of separation of variables to study the problem. We obtain several general results and, as applications, we give nontrivial exact solutions for some typical RL fractional equations such as the fractional Kadomtsev–Petviashvili equation and the fractional Langmuir chain equation. In particular, we obtain non-power functions solutions for a kind of RL time-fractional reaction–diffusion equation. In addition, we find that the separation of variables method is more suited to deal with high-dimensional nonlinear RL fractional equations because we have more freedom to choose undetermined functions. 相似文献
10.
Mehmet Senol 《理论物理通讯》2020,72(5):55003-31
In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations. 相似文献
11.
In this article,we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations.We use the improved(G’/G)-expansion function method to calculate the exact solutions to the time-and space-fractional derivative foam drainage equation and the time-and space-fractional derivative nonlinear KdV equation.This method is efficient and powerful for solving wide classes of nonlinear evolution fractional order equations. 相似文献
12.
In this paper, the Lie group classification method is performed on the fractional partial differential equation (FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact solutions to the fractional equations are presented, the compatibility of the symmetry analysis for the fractional and integer-order cases is verified. Especially, we reduce the FPDEs to the fractional ordinary differential equations (FODEs) in terms of the Erdélyi-Kober (E-K) fractional operator method, and extend the power series method for investigating exact solutions to the FPDEs. 相似文献
13.
In this Letter, we generalize the differential transform method to solve differential-difference equation for the first time. Two simple but typical examples are applied to illustrate the validity and the great potential of the generalized differential transform method in solving differential-difference equation. A Padé technique is also introduced and combined with GDTM in aim of extending the convergence area of presented series solutions. Comparisons are made between the results of the proposed method and exact solutions. Then we apply the differential transform method to the discrete KdV equation and the discrete mKdV equation, and successfully obtain solitary wave solutions. The results reveal that the proposed method is very effective and simple. We should point out that generalized differential transform method is also easy to be applied to other nonlinear differential-difference equation. 相似文献
14.
15.
In this study, we consider analytical solutions of space–time fractional derivative foam drainage equation, the nonlinear Korteweg–de Vries equation with time and space-fractional derivatives and time-fractional reaction–diffusion equation by using the extended tanh method. The fractional derivatives are defined in the modified Riemann–Liouville context. As a result, various exact analytical solutions consisting of trigonometric function solutions, kink-shaped soliton solutions and new exact solitary wave solutions are obtained. 相似文献
16.
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained. 相似文献
17.
Motivated by the widely used ansätz method and starting from the modified Riemann-Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper. 相似文献
18.
In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetsov(m ZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie's modified Riemann–Liouville sense. 相似文献
19.
Dipankar Kumar Aly R. Seadawy Atish Kumar Joardar 《Chinese Journal of Physics (Taipei)》2018,56(1):75-85
In this study, the modified Kudryashov method is used to construct new exact solutions for some conformable fractional differential equations. By implementing the conformable fractional derivative and compatible fractional complex transforms, the fractional generalized reaction duffing (RD) model equation, the fractional biological population model and the fractional diffusion reaction (DR) equation with quadratic and cubic nonlinearity are discussed. As an outcome, some new exact solutions are formally established. All solutions have been verified back into its corresponding equation with the aid of maple package program. We assure that the employed method is simple and robust for the estimation of the new exact solutions, and practically capable for reducing the size of computational work for solving a various class of fractional differential equations arising in applied mathematics, mathematical physics and biology. 相似文献
20.
提出了一种比较系统的求解非线性发展方程精确解的新方法, 即试探方程法. 以一个带5阶 导数项的非线性发展方程为例, 利用试探方程法化成初等积分形式,再利用三阶多项式的完 全判别系统求解,由此求得的精确解包括有理函数型解, 孤波解, 三角函数型周期解, 多项 式型Jacobi椭圆函数周期解和分式型Jacobi椭圆函数周期解
关键词:
试探方程法
非线性发展方程
孤波解
Jacobi椭圆函数
周期解 相似文献