메뉴 건너뛰기




Volumn 91, Issue 3, 2011, Pages 446-451

On nonlinear fractional KleinGordon equation

Author keywords

Caputo fractional derivative; Fractional Klein Gordon; Homotopy perturbation method; Iteration method; Numerical algorithm

Indexed keywords

CAPUTO FRACTIONAL DERIVATIVES; HOMOTOPY PERTURBATION METHOD; ITERATION METHOD; KLEIN-GORDON; NUMERICAL ALGORITHMS;

EID: 78049333706     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2010.04.016     Document Type: Article
Times cited : (137)

References (52)
  • 12
    • 4243530410 scopus 로고    scopus 로고
    • Mechanics with fractional derivatives
    • F. Riewe Mechanics with fractional derivatives Phys. Rev. E 55 1997 3581
    • (1997) Phys. Rev. e , vol.55 , pp. 3581
    • Riewe, F.1
  • 13
    • 0034271488 scopus 로고    scopus 로고
    • Fractional quantum mechanics
    • N. Laskin Fractional quantum mechanics Phys. Rev. E 62 2000 3135
    • (2000) Phys. Rev. e , vol.62 , pp. 3135
    • Laskin, N.1
  • 14
    • 0036887936 scopus 로고    scopus 로고
    • Chaos, fractional kinetics, and anomalous transport
    • G. M Zaslavsky Chaos, fractional kinetics, and anomalous transport Phys. Rep. 371 2002 461
    • (2002) Phys. Rep. , vol.371 , pp. 461
    • Zaslavsky, M.G.1
  • 15
    • 30544445345 scopus 로고    scopus 로고
    • Fractional sequential mechanics-models with symmetric fractional derivative
    • K. Klimek Fractional sequential mechanics-models with symmetric fractional derivative Czech. J. Phys. 55 2005 1447
    • (2005) Czech. J. Phys. , vol.55 , pp. 1447
    • Klimek, K.1
  • 16
    • 14844283120 scopus 로고    scopus 로고
    • Hamiltonian formulation of systems with linear velocities within RiemanLiouville fractional derivatives
    • S. Muslih, and D. Baleanu Hamiltonian formulation of systems with linear velocities within RiemanLiouville fractional derivatives J. Math. Anal. Appl. 304 2005 599
    • (2005) J. Math. Anal. Appl. , vol.304 , pp. 599
    • Muslih, S.1    Baleanu, D.2
  • 17
    • 23344444772 scopus 로고    scopus 로고
    • Lagrangian formulation of classical fields within RiemannLiouville fractional derivatives
    • D. Baleanu, and S. Muslih Lagrangian formulation of classical fields within RiemannLiouville fractional derivatives Phys. Scr. 72 2005 119
    • (2005) Phys. Scr. , vol.72 , pp. 119
    • Baleanu, D.1    Muslih, S.2
  • 18
    • 33845669957 scopus 로고    scopus 로고
    • Fractional Hamilton formalism within Caputo's derivative
    • D. Baleanu, and O.P. Agrawal Fractional Hamilton formalism within Caputo's derivative Czech. J. Phys. 56 2006 1087
    • (2006) Czech. J. Phys. , vol.56 , pp. 1087
    • Baleanu, D.1    Agrawal, O.P.2
  • 19
    • 33750541076 scopus 로고    scopus 로고
    • Fractional Hamiltonian analysis of higher order derivatives systems
    • D. Baleanu, S. Muslih, and K. Tas Fractional Hamiltonian analysis of higher order derivatives systems J. Math. Phys. 47 2006 103503
    • (2006) J. Math. Phys. , vol.47 , pp. 103503
    • Baleanu, D.1    Muslih, S.2    Tas, K.3
  • 21
    • 53149131751 scopus 로고    scopus 로고
    • Fractional Poisson bracket
    • A.K. Golmankhaneh Fractional Poisson bracket Turk. J. Phys. 32 2008 241
    • (2008) Turk. J. Phys. , vol.32 , pp. 241
    • Golmankhaneh, A.K.1
  • 23
    • 37549039833 scopus 로고    scopus 로고
    • HamiltonJacobi formulation of systems within Caputo's fractional derivative
    • E.M. Rabei, I. Almayteh, S.I. Muslih, and D. Baleanu HamiltonJacobi formulation of systems within Caputo's fractional derivative Phys. Scr. 77 2007 015101
    • (2007) Phys. Scr. , vol.77 , pp. 015101
    • Rabei, E.M.1    Almayteh, I.2    Muslih, S.I.3    Baleanu, D.4
  • 24
    • 34748816791 scopus 로고    scopus 로고
    • Heisenberg's equations of motion with fractional derivatives
    • E.M. Rabei, D.M. Tarawneh, S.I. Muslih, and D. Baleanu Heisenberg's equations of motion with fractional derivatives J. Vib. Cont. 13 2007 1239
    • (2007) J. Vib. Cont. , vol.13 , pp. 1239
    • Rabei, E.M.1    Tarawneh, D.M.2    Muslih, S.I.3    Baleanu, D.4
  • 25
    • 34250648556 scopus 로고    scopus 로고
    • A formulation of Noether's theorem for fractional problems of the calculus of variations
    • S.F. Gastao Frederico, and F.M.T. Delfim A formulation of Noether's theorem for fractional problems of the calculus of variations J. Math. Anal. Appl. 334 2007 834
    • (2007) J. Math. Anal. Appl. , vol.334 , pp. 834
    • Gastao Frederico, S.F.1    Delfim, F.M.T.2
  • 27
    • 0036701004 scopus 로고    scopus 로고
    • Formulation of Euler-Lagrange equations for fractional variational problems
    • O.P. Agrawal Formulation of Euler-Lagrange equations for fractional variational problems J. Math. Anal. Appl. 272 2002 368
    • (2002) J. Math. Anal. Appl. , vol.272 , pp. 368
    • Agrawal, O.P.1
  • 28
    • 42449096849 scopus 로고    scopus 로고
    • On exact solutions of a class of fractional Euler-Lagrange equations
    • D. Baleanu, and J.J. Trujillo On exact solutions of a class of fractional Euler-Lagrange equations Nonlinear Dyn. 52 2008 331
    • (2008) Nonlinear Dyn. , vol.52 , pp. 331
    • Baleanu, D.1    Trujillo, J.J.2
  • 30
    • 33745967716 scopus 로고    scopus 로고
    • Fractional calculus applications in signals and systems
    • M.D. Ortigueira, and J.A. Tenreiro Machado Fractional calculus applications in signals and systems Signal Processing 86 2006 2503
    • (2006) Signal Processing , vol.86 , pp. 2503
    • Ortigueira, M.D.1    MacHado Tenreiro, J.A.2
  • 31
    • 70350620552 scopus 로고    scopus 로고
    • The fractional quantum derivative and its integral representations
    • M.D. Ortigueira The fractional quantum derivative and its integral representations Commun. Nonlinear Sci. Numer. Simulat. 15 2010 956
    • (2010) Commun. Nonlinear Sci. Numer. Simulat. , vol.15 , pp. 956
    • Ortigueira, M.D.1
  • 32
    • 38749093369 scopus 로고    scopus 로고
    • On the relation between the fractional Brownian motion and the fractional derivatives
    • M.D. Ortigueira On the relation between the fractional Brownian motion and the fractional derivatives Phys. Lett. A 372 2008 958
    • (2008) Phys. Lett. A , vol.372 , pp. 958
    • Ortigueira, M.D.1
  • 33
    • 63449116783 scopus 로고    scopus 로고
    • Fractional derivatives: Probability interpretation and frequency response of rational approximations
    • J.A. Tenreiro Machado Fractional derivatives: probability interpretation and frequency response of rational approximations Commun. Nonlinear Sci. Numer. Simul. 14 2009 3492
    • (2009) Commun. Nonlinear Sci. Numer. Simul. , vol.14 , pp. 3492
    • MacHado Tenreiro, J.A.1
  • 35
    • 0025548782 scopus 로고
    • A review of the decomposition method and some recent results for nonlinear equation
    • G. Adomian A review of the decomposition method and some recent results for nonlinear equation Math. Comput. Model. 13 1992 17
    • (1992) Math. Comput. Model. , vol.13 , pp. 17
    • Adomian, G.1
  • 36
    • 0002095007 scopus 로고
    • Noise terms in decomposition series solution
    • G. Adomian, and R. Rach Noise terms in decomposition series solution Comput. Math. Appl. 24 1992 61
    • (1992) Comput. Math. Appl. , vol.24 , pp. 61
    • Adomian, G.1    Rach, R.2
  • 37
    • 10344238128 scopus 로고    scopus 로고
    • Adomian decomposition: A tool for solving a system of fractional differential equations
    • V. Daftardar-Gejji, and H. Jafari Adomian decomposition: a tool for solving a system of fractional differential equations J. Math. Anal. 301 2005 508
    • (2005) J. Math. Anal. , vol.301 , pp. 508
    • Daftardar-Gejji, V.1    Jafari, H.2
  • 38
    • 38049021511 scopus 로고    scopus 로고
    • On the solution of the fractional nonlinear Schrodinger equation
    • S.Z. Rida, H.M. El-Sherbiny, and A.A.M. Arafa On the solution of the fractional nonlinear Schrodinger equation Phys. Lett. A 372 2008 553
    • (2008) Phys. Lett. A , vol.372 , pp. 553
    • Rida, S.Z.1    El-Sherbiny, H.M.2    Arafa, A.A.M.3
  • 39
    • 0033702384 scopus 로고    scopus 로고
    • A coupling method of homotopy technique and perturbation technique for nonlinear problems
    • J.H. He A coupling method of homotopy technique and perturbation technique for nonlinear problems Int. J. Non-Linear Mech. 35 2000 37
    • (2000) Int. J. Non-Linear Mech. , vol.35 , pp. 37
    • He, J.H.1
  • 40
    • 3943092529 scopus 로고    scopus 로고
    • Comparison of homotopy perturbation method and homotopy analysis method
    • J.H. He Comparison of homotopy perturbation method and homotopy analysis method Appl. Math. Comput. 156 2004 527
    • (2004) Appl. Math. Comput. , vol.156 , pp. 527
    • He, J.H.1
  • 42
    • 0037440579 scopus 로고    scopus 로고
    • Homotopy perturbation method: A new nonlinear analytical technique
    • J.H. He Homotopy perturbation method: a new nonlinear analytical technique Appl. Math. Comput. 135 2003 73
    • (2003) Appl. Math. Comput. , vol.135 , pp. 73
    • He, J.H.1
  • 43
    • 1242287587 scopus 로고    scopus 로고
    • The homotopy perturbation method for nonlinear oscillators with discontinuities
    • J.H. He The homotopy perturbation method for nonlinear oscillators with discontinuities Appl. Math. Comput. 151 2004 287
    • (2004) Appl. Math. Comput. , vol.151 , pp. 287
    • He, J.H.1
  • 44
    • 63449096068 scopus 로고    scopus 로고
    • Application of homotopy-perturbation method to KleinGordon and sine-Gordon equations
    • M.S.H. Chowdhury, and I. Hashim Application of homotopy-perturbation method to KleinGordon and sine-Gordon equations Chaos, Solitons and Fractals 39 2009 1928
    • (2009) Chaos, Solitons and Fractals , vol.39 , pp. 1928
    • Chowdhury, M.S.H.1    Hashim, I.2
  • 45
    • 61349186917 scopus 로고    scopus 로고
    • Matrix approach to discrete fractional calculus II: Partial fractional differential equations
    • I. Podlubny, A.V. Chechkin, T. Skovranek, Y.Q. Chen, and B.M. Vinagre Matrix approach to discrete fractional calculus II: partial fractional differential equations J. Comput. Phys. 228 2009 3137
    • (2009) J. Comput. Phys. , vol.228 , pp. 3137
    • Podlubny, I.1    Chechkin, A.V.2    Skovranek, T.3    Chen, Y.Q.4    Vinagre, B.M.5
  • 46
    • 67449110445 scopus 로고    scopus 로고
    • Chaos in the fractional-order Volta's system: Modeling and simulation
    • I. Petras Chaos in the fractional-order Volta's system: modeling and simulation Nonlinear Dyn. 57 2009 157
    • (2009) Nonlinear Dyn. , vol.57 , pp. 157
    • Petras, I.1
  • 48
    • 0038577058 scopus 로고    scopus 로고
    • The decomposition method for studying the KleinGordon equation
    • S. El-Sayed The decomposition method for studying the KleinGordon equation Chaos, Solitons and Fractals 18 2003 1025
    • (2003) Chaos, Solitons and Fractals , vol.18 , pp. 1025
    • El-Sayed, S.1
  • 50
    • 25144450080 scopus 로고    scopus 로고
    • The tanh method: Exact solutions of the sine-Gordon and the sinh-Gordon equations
    • A.M. Wazwaz The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations Appl. Math. Comput. 167 2005 1196
    • (2005) Appl. Math. Comput. , vol.167 , pp. 1196
    • Wazwaz, A.M.1
  • 51
    • 43549101930 scopus 로고    scopus 로고
    • The variational iteration method for studying the KleinGordon equation
    • E. Yusufoglu The variational iteration method for studying the KleinGordon equation Appl. Math. Lett. 21 2008 669
    • (2008) Appl. Math. Lett. , vol.21 , pp. 669
    • Yusufoglu, E.1
  • 52
    • 35349016929 scopus 로고    scopus 로고
    • Numerical solution of sine-Gordon equation by variational iteration method
    • Z. Odibat, and S.A. Momani Numerical solution of sine-Gordon equation by variational iteration method Phys. Lett. A 370 2007 437
    • (2007) Phys. Lett. A , vol.370 , pp. 437
    • Odibat, Z.1    Momani, S.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.