分数阶时间偏微分差分方程新的精确解
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摘要
基于指数函数展开法,借助符号计算系统Maple,构造了时间-分数阶偏微分差分方程新的指数形式解,结果有助于理解时间-分数阶偏微分差分方程对应的数学模型,其指数函数展开法也可以用来构造其他分数阶微分差分方程的精确解.
Constructing exact solutions is an important branch to study fractional partial differential-difference equations. Based on exponential functions expansion method and the aid of symbolic computation system,Maple,new exponential function solutions of time-fractional partial differential-difference equations are obtained. These new results can help us to understand the mathematical model of the time-fractional partial differential-difference equations. This method can be used to solve other fractional partial differential-difference equations.
Constructing exact solutions is an important branch to study fractional partial differential-difference equations. Based on exponential functions expansion method and the aid of symbolic computation system,Maple,new exponential function solutions of time-fractional partial differential-difference equations are obtained. These new results can help us to understand the mathematical model of the time-fractional partial differential-difference equations. This method can be used to solve other fractional partial differential-difference equations.
引文
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[2] Wang Zhen,Zhang Hongqing. New exact solutions to some difference differential equations[J]. Chinese Physics,2006,15(10):2210-2215.
[3] Zheng Bin,Wen Chuanbao. Exact solutions for fractional partial differential equations by a new fractional sub-equation method[J].Advances in Difference Equations,2013,2013(1):1-12.
[4] Zheng Bin. A new fractional Jacobi elliptic equation method for solving fractional partial differential equations[J]. Advances in Difference Equations,2014,2014(1):1-11.
[5] Feng Qinghua. Exact solutions for fractional differential-difference equations by an extended Riccati Sub-ODE Method[J].Communications in Theoretical Physics,2013,59(5):521-527.
[6] Mostafa Eslami. Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations[J]. Applied Mathematics and Computation,2016,285(1):141-148.
[7] Ahmet Bekira,zkan Günerb,Burcu Ayhana. Exact solutions of some systems of fractional differential-difference equations[J].Mathematical Methods in the Applied Sciences,2014,38(17):3807-3817.
[8] Ismail Aslan. An analytic approach to a class of fractional differential-difference equations of rational type via symbolic computation[J]. Mathematical Methods in the Applied Sciences,2014,38(1):27-36.
[9] Narita K. New discrete modified Kd V equation[J]. Progress of Theoretical Physics,1991,86(4):817-824.
[10] Liu Chengshi. Counterexamples on Jumarie’s two basic fractional calculus formulae[J]. Communications in Nonlinear Science and Numerical Simulation,2015,22(1-3):92-94.
[11]套格图桑,斯仁道尔吉,李姝敏.基于指数函数展开法构造非线性差分微分方程新的精确解[J].内蒙古大学学报(自然科学版),2010,4l(4):361-367.
[12] He Jihuan,Elagan,S K Li,et al. Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus[J]. Physics Letters A,2012,376(4):257-259.
[13] He Jihuan,Li Zhengbiao,Wang Qingli. A new fractional derivative and its application to explanation of polar bear hairs[J].Journal of King Saud University Science,2016,28(2):190-192.
[14] Ozkan Guner. Exp-function method and fractional complex transform for space-time fractional KP-BBM equation[J].Communications in Theoretical Physics,2017,68(2):149-154.
[2] Wang Zhen,Zhang Hongqing. New exact solutions to some difference differential equations[J]. Chinese Physics,2006,15(10):2210-2215.
[3] Zheng Bin,Wen Chuanbao. Exact solutions for fractional partial differential equations by a new fractional sub-equation method[J].Advances in Difference Equations,2013,2013(1):1-12.
[4] Zheng Bin. A new fractional Jacobi elliptic equation method for solving fractional partial differential equations[J]. Advances in Difference Equations,2014,2014(1):1-11.
[5] Feng Qinghua. Exact solutions for fractional differential-difference equations by an extended Riccati Sub-ODE Method[J].Communications in Theoretical Physics,2013,59(5):521-527.
[6] Mostafa Eslami. Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations[J]. Applied Mathematics and Computation,2016,285(1):141-148.
[7] Ahmet Bekira,zkan Günerb,Burcu Ayhana. Exact solutions of some systems of fractional differential-difference equations[J].Mathematical Methods in the Applied Sciences,2014,38(17):3807-3817.
[8] Ismail Aslan. An analytic approach to a class of fractional differential-difference equations of rational type via symbolic computation[J]. Mathematical Methods in the Applied Sciences,2014,38(1):27-36.
[9] Narita K. New discrete modified Kd V equation[J]. Progress of Theoretical Physics,1991,86(4):817-824.
[10] Liu Chengshi. Counterexamples on Jumarie’s two basic fractional calculus formulae[J]. Communications in Nonlinear Science and Numerical Simulation,2015,22(1-3):92-94.
[11]套格图桑,斯仁道尔吉,李姝敏.基于指数函数展开法构造非线性差分微分方程新的精确解[J].内蒙古大学学报(自然科学版),2010,4l(4):361-367.
[12] He Jihuan,Elagan,S K Li,et al. Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus[J]. Physics Letters A,2012,376(4):257-259.
[13] He Jihuan,Li Zhengbiao,Wang Qingli. A new fractional derivative and its application to explanation of polar bear hairs[J].Journal of King Saud University Science,2016,28(2):190-192.
[14] Ozkan Guner. Exp-function method and fractional complex transform for space-time fractional KP-BBM equation[J].Communications in Theoretical Physics,2017,68(2):149-154.