一类非线性分数阶发展方程的新精确解
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摘要
利用exp(-Φ(ξ)展开法,分别得到非线性分数阶Phi-4方程,非线性分数阶foam drainage方程,非线性分数阶SRLW方程的新精确解.实践证明,方法简洁方便,对于研究非线性分数阶发展方程具有十分重要的意义.
Using exp(-Φ(ξ))-expansion method,the nonlinear fractional Phi-4 equation were obtained by nonlinear fractional order foam drainage equation,the new exact solutions of the nonlinear fractional SRLW equation.The practice proves that this method is simple and convenient,has very important significance for the research of nonlinear fractional evolution equations.
Using exp(-Φ(ξ))-expansion method,the nonlinear fractional Phi-4 equation were obtained by nonlinear fractional order foam drainage equation,the new exact solutions of the nonlinear fractional SRLW equation.The practice proves that this method is simple and convenient,has very important significance for the research of nonlinear fractional evolution equations.
引文
[1]Ozkan Guner.Singular and non-topolotical soliton solutions for nonlinear fractional differential equations[J].Chin Phys B,2015,24(10):1002011-1002016.
[2]Emad A.-B.Abdel-Salam,Gamal F.Hassan.Multi-wave solutions of the space-time fractional Burgers and SharmarTasso-Olver equations[J].Ain Shams Engineering Journal,2016,7:463-472.
[3]Yusuf Pandir and Hasan Huseyin Duzgun.New Exact Solutions of Time Fractional Gardner Equation by Using New Version of F-ExpansionMethod[J].Commun Theor Phys,2017,67:9-14.
[4]FENG Qinghua.A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations[J].Commun Theor Phys,2014,62:167-172.
[5]Huang Qing,Wang LiZhen,Zuo SuLi.Consistent Riccati Expansion Method and Its Applications to Nonlinear Fractional Partial Differential Equations[J].Commun Theor Phys,2016,65:177-184.
[6]Melike Kaplan,Arzu Akbulutand Ahmet Bekir.Solving Space-Time Fractional Differential Equations by Using Modified Simple Equation Method[J].Commun Theor Phys,2016,65:563-568.
[7]Ozkan Guner,and Ahmet Bekir.(Bright and dark soliton solutions for some nonlinear fractional differential equations[J].Chin Phys B,2016,25(3):0302031-03020318.
[8]Xing L 0,Wen-Xiu Ma,Jun Yu,Fuhong Lin.Envelope bright-and dark-soliton solutions for the Gerdjikov-Ivanov model[J].Nonlinear Dyn,2015,82:1211-1220.
[9]Omar Abu Arqub,Ahmad El-Ajou,Shaher Momani.Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations[J].Applied Mathematics Letters Journal of Computational Physics,2015,293:385-399.
[10]Xing Lü,Wen-Xiu Mab,Chaudry Masood Khalique.A direct bilinear B?cklund transformation of a(2+1)-dimensional Korteweg-de Vries-like model[J].Applied Mathematics Letters,2015,50:37-42.
[11]Ozkan Guner,Hasan Atik.Soliton solution of fractional-order nonlinear differential equations based on the exp-function method[J].Optik,2016,127:10076-10083.
[12]Muhammad Arshad,Dianchen Lu,Jun Wang.(N+1)-dimensional fractional reduce d differential transform method for fractional order partial differential equations[J].Commun Nonlinear Sci Numer Simulat,2017,48:509-519.
[13]Alper Korkmaz.Exact solutions of space-time fractional EW and modified EW equations[J].Chaos,Solitons and Fractals,2017,96:132-138.
[14]Jin Hyuk Choi,Hyunsoo Kim.Soliton solutions for the space-time nonlinear partial differential equations with fractional-orders[J].Chinese Journal of Physics,2017,55:556-565.
[15]Zhang Sheng,Zhang Hongqing.Fractional sub-equation method and itsapplications to nonlinear fractional PDEs[J].Phys Lett A,2011,375:1069-1073.
[16]Mehmet Ekici.Soliton and other solutions of nonlinear time fractional parabolic equations using extended G'/G-expansion method[J].Optik,2017,130:1312-1319.
[17]Kamruzzaman Khan,M.Ali Akbar.Exact traveling wave solutions of Kadomtsev Petviashvili equation[J].Journal of the Egyptian Mathematical Society,2015,23:278-281.
[18]Arzu Akbulut,Melike Kaplan,Filiz Tascan.The investigation of exact solutions of nonlinear partial differential equations by using exp(-Φ(ξ))method[J].Optik,2017,132:382-387.
[19]Md.Nur Alam Hafez M G,Ali Akbar M.Harun-Or-Roshid. Exact traveling wave solutions to the(3+1)-dimensional mKdV-ZK and the(2+1)-dimensional Burgers equations via exp(-Φ(ξ))-expansion method[J].Alexandria Engineering Journal,2015,54:635-644.
[20]Harun-Or-Roshid,Md.Azizur Rahman.The exp(-Φ(ξ))-expansion method with application in the(1+1)-dimensional classical Boussinesq equations[J].Results in Physics,2014,4:150-155.
[21]Jumarie G.Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution[J].Appl Math Comput,2007,24:31-38.
[22]Hira Tariq,Ghazala Akram.New approach for exact solutions of time fractional Cahn-Allen equation and time fractional Phi-4 equation[J].Physica A,2017,473:352-362.
[23]Khaled A.Gepreel and Saleh Omran.Exact solutions for nonlinear partial fractional differential equations[J].Chin Phys B,2012,21(11):110204.
[24]Syed Tauseef Mohyud-Din Sadaf Bibi.Exact solutions for nonlinear fractional differential equations using exponential rational function method[J].Opt Quant Electron,2017,49:64.
[2]Emad A.-B.Abdel-Salam,Gamal F.Hassan.Multi-wave solutions of the space-time fractional Burgers and SharmarTasso-Olver equations[J].Ain Shams Engineering Journal,2016,7:463-472.
[3]Yusuf Pandir and Hasan Huseyin Duzgun.New Exact Solutions of Time Fractional Gardner Equation by Using New Version of F-ExpansionMethod[J].Commun Theor Phys,2017,67:9-14.
[4]FENG Qinghua.A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations[J].Commun Theor Phys,2014,62:167-172.
[5]Huang Qing,Wang LiZhen,Zuo SuLi.Consistent Riccati Expansion Method and Its Applications to Nonlinear Fractional Partial Differential Equations[J].Commun Theor Phys,2016,65:177-184.
[6]Melike Kaplan,Arzu Akbulutand Ahmet Bekir.Solving Space-Time Fractional Differential Equations by Using Modified Simple Equation Method[J].Commun Theor Phys,2016,65:563-568.
[7]Ozkan Guner,and Ahmet Bekir.(Bright and dark soliton solutions for some nonlinear fractional differential equations[J].Chin Phys B,2016,25(3):0302031-03020318.
[8]Xing L 0,Wen-Xiu Ma,Jun Yu,Fuhong Lin.Envelope bright-and dark-soliton solutions for the Gerdjikov-Ivanov model[J].Nonlinear Dyn,2015,82:1211-1220.
[9]Omar Abu Arqub,Ahmad El-Ajou,Shaher Momani.Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations[J].Applied Mathematics Letters Journal of Computational Physics,2015,293:385-399.
[10]Xing Lü,Wen-Xiu Mab,Chaudry Masood Khalique.A direct bilinear B?cklund transformation of a(2+1)-dimensional Korteweg-de Vries-like model[J].Applied Mathematics Letters,2015,50:37-42.
[11]Ozkan Guner,Hasan Atik.Soliton solution of fractional-order nonlinear differential equations based on the exp-function method[J].Optik,2016,127:10076-10083.
[12]Muhammad Arshad,Dianchen Lu,Jun Wang.(N+1)-dimensional fractional reduce d differential transform method for fractional order partial differential equations[J].Commun Nonlinear Sci Numer Simulat,2017,48:509-519.
[13]Alper Korkmaz.Exact solutions of space-time fractional EW and modified EW equations[J].Chaos,Solitons and Fractals,2017,96:132-138.
[14]Jin Hyuk Choi,Hyunsoo Kim.Soliton solutions for the space-time nonlinear partial differential equations with fractional-orders[J].Chinese Journal of Physics,2017,55:556-565.
[15]Zhang Sheng,Zhang Hongqing.Fractional sub-equation method and itsapplications to nonlinear fractional PDEs[J].Phys Lett A,2011,375:1069-1073.
[16]Mehmet Ekici.Soliton and other solutions of nonlinear time fractional parabolic equations using extended G'/G-expansion method[J].Optik,2017,130:1312-1319.
[17]Kamruzzaman Khan,M.Ali Akbar.Exact traveling wave solutions of Kadomtsev Petviashvili equation[J].Journal of the Egyptian Mathematical Society,2015,23:278-281.
[18]Arzu Akbulut,Melike Kaplan,Filiz Tascan.The investigation of exact solutions of nonlinear partial differential equations by using exp(-Φ(ξ))method[J].Optik,2017,132:382-387.
[19]Md.Nur Alam Hafez M G,Ali Akbar M.Harun-Or-Roshid. Exact traveling wave solutions to the(3+1)-dimensional mKdV-ZK and the(2+1)-dimensional Burgers equations via exp(-Φ(ξ))-expansion method[J].Alexandria Engineering Journal,2015,54:635-644.
[20]Harun-Or-Roshid,Md.Azizur Rahman.The exp(-Φ(ξ))-expansion method with application in the(1+1)-dimensional classical Boussinesq equations[J].Results in Physics,2014,4:150-155.
[21]Jumarie G.Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution[J].Appl Math Comput,2007,24:31-38.
[22]Hira Tariq,Ghazala Akram.New approach for exact solutions of time fractional Cahn-Allen equation and time fractional Phi-4 equation[J].Physica A,2017,473:352-362.
[23]Khaled A.Gepreel and Saleh Omran.Exact solutions for nonlinear partial fractional differential equations[J].Chin Phys B,2012,21(11):110204.
[24]Syed Tauseef Mohyud-Din Sadaf Bibi.Exact solutions for nonlinear fractional differential equations using exponential rational function method[J].Opt Quant Electron,2017,49:64.