메뉴 건너뛰기




Volumn 2012, Issue , 2012, Pages

Solving the fractional nonlinear Klein-Gordon equation by means of the homotopy analysis method

Author keywords

analytical solutions; fractional nonlinear Klein Gordon equations; homotopy analysis method

Indexed keywords


EID: 84873401814     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1186/1687-1847-2012-187     Document Type: Article
Times cited : (42)

References (24)
  • 1
    • 78049333706 scopus 로고    scopus 로고
    • On nonlinear fractional Klein-Gordon equation
    • 1203.94031 10.1016/j.sigpro.2010.04.016
    • Golmankhaneh AK, Golmankhaneh AK, Baleanu D: On nonlinear fractional Klein-Gordon equation. Signal Process. 2011, 91:446-451.
    • (2011) Signal Process , vol.91 , pp. 446-451
    • Golmankhaneh, A.K.1    Golmankhaneh, A.K.2    Baleanu, D.3
  • 2
    • 0012835662 scopus 로고
    • PhD thesis, Shanghai Jiao Tong University, Shanghai, China (1992)Liao, S-J: The proposed homotopy analysis technique for the solution of nonlinear problems. PhD thesis, Shanghai Jiao Tong University, Shanghai, China
    • Liao, S-J: The proposed homotopy analysis technique for the solution of nonlinear problems. PhD thesis, Shanghai Jiao Tong University, Shanghai, China (1992)Liao, S-J: The proposed homotopy analysis technique for the solution of nonlinear problems. PhD thesis, Shanghai Jiao Tong University, Shanghai, China (1992)
    • (1992) The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems
    • Liao, S.-J.1
  • 3
    • 0000615571 scopus 로고
    • An approximate solution technique not depending on small parameters: A special example
    • 0837.76073 10.1016/0020-7462(94)00054-E
    • Liao S-J: An approximate solution technique not depending on small parameters: a special example. Int. J. Non-Linear Mech. 1995,30(3):371-380.
    • (1995) Int. J. Non-Linear Mech , vol.30 , Issue.3 , pp. 371-380
    • Liao, S.-J.1
  • 4
    • 0031232480 scopus 로고    scopus 로고
    • A kind of approximate solution technique which does not depend upon small parameters - II. An application in fluid mechanics
    • PII S0020746296001011
    • Liao S-J: A kind of approximate solution technique which does not depend upon small parameters - II. An application in fluid mechanics. Int. J. Non-Linear Mech. 1997,32(5):815-822. (Pubitemid 127413762)
    • (1997) International Journal of Non-Linear Mechanics , vol.32 , Issue.5 , pp. 815-822
    • Liao, S.-J.1
  • 6
    • 63449096068 scopus 로고    scopus 로고
    • Application of homotopy-perturbation method to Klein-Gordon and sine-Gordon equations
    • 2514578 1197.65164 10.1016/j.chaos.2007.06.091
    • Chowdhury MSH, Hashim I: Application of homotopy-perturbation method to Klein-Gordon and sine-Gordon equations. Chaos Solitons Fractals 2009, 39:1928.
    • (2009) Chaos Solitons Fractals , vol.39 , pp. 1928
    • Chowdhury, M.S.H.1    Hashim, I.2
  • 7
    • 55549136027 scopus 로고    scopus 로고
    • Notes on the homotopy analysis method: Some definitions and theorems
    • 2468931 1221.65126 10.1016/j.cnsns.2008.04.013
    • Liao S-J: Notes on the homotopy analysis method: some definitions and theorems. Commun. Nonlinear Sci. Numer. Simul. 2009,14(4):983-997.
    • (2009) Commun. Nonlinear Sci. Numer. Simul , vol.14 , Issue.4 , pp. 983-997
    • Liao, S.-J.1
  • 8
    • 48749083737 scopus 로고    scopus 로고
    • Explicit solution to the exact Riemann problem and application in nonlinear shallow-water equations
    • 2436345 1210.76033 10.1002/fld.1696
    • Wu Y, Cheung KF: Explicit solution to the exact Riemann problem and application in nonlinear shallow-water equations. Int. J. Numer. Methods Fluids 2008,57(11):1649-1668.
    • (2008) Int. J. Numer. Methods Fluids , vol.57 , Issue.11 , pp. 1649-1668
    • Wu, Y.1    Cheung, K.F.2
  • 9
    • 59849106542 scopus 로고    scopus 로고
    • Series solutions of time-fractional PDEs by homotopy analysis method
    • 2008 Article ID 686512. doi:10.1155/2008/686512
    • Abdulaziz O, Hashim I, Saif A: Series solutions of time-fractional PDEs by homotopy analysis method. Differ. Equ. Nonlinear Mech. 2008., 2008: Article ID 686512. doi:10.1155/2008/686512
    • (2008) Differ. Equ. Nonlinear Mech
    • Abdulaziz, O.1    Hashim, I.2    Saif, A.3
  • 10
    • 34347339334 scopus 로고    scopus 로고
    • Application of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation
    • 2320873 1209.65115 10.1016/j.physleta.2007.02.083
    • Song L, Zhang H: Application of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation. Phys. Lett. A 2007,367(1-2):88-94.
    • (2007) Phys. Lett. A , vol.367 , Issue.1-2 , pp. 88-94
    • Song, L.1    Zhang, H.2
  • 11
    • 64549148828 scopus 로고    scopus 로고
    • Series solutions of non-linear Riccati differential equations with fractional order
    • 2517912 1197.34006 10.1016/j.chaos.2007.04.018
    • Cang J, Tan Y, Xu H, Liao S-J: Series solutions of non-linear Riccati differential equations with fractional order. Chaos Solitons Fractals 2009, 40:1-9.
    • (2009) Chaos Solitons Fractals , vol.40 , pp. 1-9
    • Cang, J.1    Tan, Y.2    Xu, H.3    Liao, S.-J.4
  • 12
    • 50249146464 scopus 로고    scopus 로고
    • Homotopy analysis method for fractional IVPs
    • 2449879 1221.65277 10.1016/j.cnsns.2007.09.014
    • Hashim I, Abdulaziz O, Momani S: Homotopy analysis method for fractional IVPs. Commun. Nonlinear Sci. Numer. Simul. 2009,14(3):674-684.
    • (2009) Commun. Nonlinear Sci. Numer. Simul , vol.14 , Issue.3 , pp. 674-684
    • Hashim, I.1    Abdulaziz, O.2    Momani, S.3
  • 13
    • 65449123574 scopus 로고    scopus 로고
    • Solving the fractional BBM-Burgers equation using the homotopy analysis method
    • 2531252 1198.65205 10.1016/j.chaos.2007.09.042
    • Song L, Zhang H: Solving the fractional BBM-Burgers equation using the homotopy analysis method. Chaos Solitons Fractals 2009, 40:1616-1622.
    • (2009) Chaos Solitons Fractals , vol.40 , pp. 1616-1622
    • Song, L.1    Zhang, H.2
  • 14
    • 84873343931 scopus 로고    scopus 로고
    • Approximate analytical solutions of the Klein-Gordon equation by means of the homotopy analysis method
    • Alomari AK, Noorani MSM, Nazar RM: Approximate analytical solutions of the Klein-Gordon equation by means of the homotopy analysis method. JQMA 2008,4(1):45-57.
    • (2008) JQMA , vol.4 , Issue.1 , pp. 45-57
    • Alomari, A.K.1    Noorani, M.S.M.2    Nazar, R.M.3
  • 15
    • 58149490845 scopus 로고    scopus 로고
    • Series solutions of systems of nonlinear fractional differential equations
    • 2470382 1187.34007 10.1007/s10440-008-9271-x
    • Bataineh AS, Alomari AK, Noorani MSM, Hashim I, Nazar R: Series solutions of systems of nonlinear fractional differential equations. Acta Appl. Math. 2009,105(2):189-198.
    • (2009) Acta Appl. Math , vol.105 , Issue.2 , pp. 189-198
    • Bataineh, A.S.1    Alomari, A.K.2    Noorani, M.S.M.3    Hashim, I.4    Nazar, R.5
  • 16
    • 38849190109 scopus 로고    scopus 로고
    • Analysis of a time fractional wave-like equation with the homotopy analysis method
    • 2396273 1217.35111 10.1016/j.physleta.2007.09.039
    • Xu H, Cang J: Analysis of a time fractional wave-like equation with the homotopy analysis method. Phys. Lett. A 2008,372(8):1250-1255.
    • (2008) Phys. Lett. A , vol.372 , Issue.8 , pp. 1250-1255
    • Xu, H.1    Cang, J.2
  • 17
    • 55549139469 scopus 로고    scopus 로고
    • Analysis of nonlinear fractional partial differential equations with the homotopy analysis method
    • 2468947 1221.65286 10.1016/j.cnsns.2008.04.008
    • Xu H, Liao S-J, You X-C: Analysis of nonlinear fractional partial differential equations with the homotopy analysis method. Commun. Nonlinear Sci. Numer. Simul. 2009,14(4):1152-1156.
    • (2009) Commun. Nonlinear Sci. Numer. Simul , vol.14 , Issue.4 , pp. 1152-1156
    • Xu, H.1    Liao, S.-J.2    You, X.-C.3
  • 18
    • 61849114184 scopus 로고    scopus 로고
    • Differential transform method for solving the linear and nonlinear Klein-Gordon equation
    • 2678291 1198.81038 10.1016/j.cpc.2008.11.012
    • Ravi Kanth ASV, Aruna K: Differential transform method for solving the linear and nonlinear Klein-Gordon equation. Comput. Phys. Commun. 2009, 180:708-711.
    • (2009) Comput. Phys. Commun , vol.180 , pp. 708-711
    • Ravi Kanth, A.S.V.1    Aruna, K.2
  • 19
    • 56049100715 scopus 로고    scopus 로고
    • Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation
    • 2474460 1221.65278 10.1016/j.cnsns.2008.05.008
    • Jafari H, Seifi S: Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation. Commun. Nonlinear Sci. Numer. Simul. 2009,14(5):2006-2012.
    • (2009) Commun. Nonlinear Sci. Numer. Simul , vol.14 , Issue.5 , pp. 2006-2012
    • Jafari, H.1    Seifi, S.2
  • 20
    • 56049106098 scopus 로고    scopus 로고
    • Solving a system of nonlinear fractional partial differential equations using homotopy analysis method
    • 2474456 1221.35439 10.1016/j.cnsns.2008.06.019
    • Jafari H, Seifi S: Solving a system of nonlinear fractional partial differential equations using homotopy analysis method. Commun. Nonlinear Sci. Numer. Simul. 2009,14(5):1962-1969.
    • (2009) Commun. Nonlinear Sci. Numer. Simul , vol.14 , Issue.5 , pp. 1962-1969
    • Jafari, H.1    Seifi, S.2
  • 22
    • 0001799540 scopus 로고
    • Über den fundamental Satz in der Theorie der Funktionen
    • 1555014 JFM 36.0471.01 10.1007/BF02403202
    • Wiman A: Über den fundamental Satz in der Theorie der Funktionen. Acta Math. 1905, 29:191-201.
    • (1905) Acta Math , vol.29 , pp. 191-201
    • Wiman, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.