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Volumn 62, Issue 3, 2011, Pages 1522-1530

A generalized fractional KN equation hierarchy and its fractional Hamiltonian structure

Author keywords

Fractional; Hamiltonian structure; KN equation hierarchy

Indexed keywords

DIFFERENTIAL FORMS; FRACTIONAL; FRACTIONAL ORDER; GENERALIZED HAMILTONIANS; HAMILTONIAN STRUCTURES; INTEGRABLE HIERARCHY; KN EQUATION HIERARCHY; RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES; SOLITON EQUATION; TRACE IDENTITIES;

EID: 79961005744     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.04.043     Document Type: Article
Times cited : (6)

References (65)
  • 3
    • 0036887936 scopus 로고    scopus 로고
    • Fractional kinetics and anomalous transport
    • G.M. Zaslavsky Fractional kinetics and anomalous transport Phys. Rep. 371 2002 461 580
    • (2002) Phys. Rep. , vol.371 , pp. 461-580
    • Zaslavsky, G.M.1
  • 5
    • 19944384253 scopus 로고    scopus 로고
    • Dynamics with low-level fractionality
    • V.E. Tarasov, and G.M. Zaslavsky Dynamics with low-level fractionality Physica A 354 2005 249 261
    • (2005) Physica A , vol.354 , pp. 249-261
    • Tarasov, V.E.1    Zaslavsky, G.M.2
  • 6
    • 1842535435 scopus 로고    scopus 로고
    • Fractional FokkerPlanck equation for fractal media
    • V.E. Tarasov Fractional FokkerPlanck equation for fractal media Chaos 14 2004 123 127
    • (2004) Chaos , vol.14 , pp. 123-127
    • Tarasov, V.E.1
  • 7
    • 41349084525 scopus 로고    scopus 로고
    • Fractional systems and fractional Bogoliubov hierarchy equations
    • V.E. Tarasov Fractional systems and fractional Bogoliubov hierarchy equations Phys. Rev. E 71 2005 011102
    • (2005) Phys. Rev. e , vol.71 , pp. 011102
    • Tarasov, V.E.1
  • 8
    • 20444376273 scopus 로고    scopus 로고
    • Fractional Liouville and BBGKI equations
    • V.E. Tarasov Fractional Liouville and BBGKI equations J. Phys.: Conf. Ser. 7 2005 17 33
    • (2005) J. Phys.: Conf. Ser. , vol.7 , pp. 17-33
    • Tarasov, V.E.1
  • 9
    • 0022492943 scopus 로고
    • Realization of the generalized transfer in a medium with fractal geometry
    • R. Nigmatullin The realization of the generalized transfer in a medium with fractal geometry Phys. Status Solidi b 133 1986 425 430 (Pubitemid 16505297)
    • (1986) Physica Status Solidi (B) Basic Research , vol.133 , Issue.1 , pp. 425-430
    • Nigmatullin, R.R.1
  • 11
    • 4043151477 scopus 로고    scopus 로고
    • The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics
    • R. Metzler, and J. Klafter The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics J. Phys. A 37 2004 161 208
    • (2004) J. Phys. A , vol.37 , pp. 161-208
    • Metzler, R.1    Klafter, J.2
  • 27
    • 0022660581 scopus 로고
    • On the fractional calculus model of viscoelastic behavior
    • DOI 10.1122/1.549887
    • R.L. Bagley, and P.J. Torvik On the fractional calculus model of viscoelastic behavior J. Rheol. 30 1 1986 133 155 (Pubitemid 16535851)
    • (1986) Journal of Rheology , vol.30 , Issue.1 , pp. 133-155
    • Bagley, R.L.1    Torvik, P.J.2
  • 28
    • 0030575463 scopus 로고    scopus 로고
    • Analysis of four-parameter fractional derivative model of real solid materials
    • DOI 10.1006/jsvi.1996.0406
    • T. Pritz Analysis of four-parameter fractional derivative model of real solid materials J. Sound Vib. 195 1 1996 103 115 (Pubitemid 126387254)
    • (1996) Journal of Sound and Vibration , vol.195 , Issue.1 , pp. 103-115
    • Pritz, T.1
  • 29
    • 0036701004 scopus 로고    scopus 로고
    • Fractional variational calculus in terms of Riesz fractional derivatives
    • O.P. Agrawal Fractional variational calculus in terms of Riesz fractional derivatives J. Math. Anal. Appl. 272 2002 368 379
    • (2002) J. Math. Anal. Appl. , vol.272 , pp. 368-379
    • Agrawal, O.P.1
  • 32
    • 23344444772 scopus 로고    scopus 로고
    • Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives
    • D. Baleanu, and S. Muslih Lagrangian, formulation of classical fields within Riemann-Liouville fractional derivatives Phys. Scr. 72 2005 119 121 (Pubitemid 41101668)
    • (2005) Physica Scripta , vol.72 , Issue.2-3 , pp. 119-121
    • Baleanu, D.1    Muslih, S.I.2
  • 33
    • 15544380308 scopus 로고    scopus 로고
    • Fractional trigonometry and the spiral functions
    • DOI 10.1007/s11071-004-3745-9
    • C.F. Lorenzo, and T.T. Hartley Fractional trigonometry and the spiral functions Nonlinear Dynam. 38 2004 23 60 (Pubitemid 40400606)
    • (2004) Nonlinear Dynamics , vol.38 , Issue.1-4 , pp. 23-60
    • Lorenzo, C.F.1    Hartley, T.T.2
  • 34
    • 34250648556 scopus 로고    scopus 로고
    • A formulation of Noether's theorem for fractional problems of the calculus of variations
    • G.S.F. Frederico, and D.F.M. Torres A formulation of Noether's theorem for fractional problems of the calculus of variations J. Math. Anal. Appl. 334 2007 834 846
    • (2007) J. Math. Anal. Appl. , vol.334 , pp. 834-846
    • Frederico, G.S.F.1    Torres, D.F.M.2
  • 35
    • 53149131751 scopus 로고    scopus 로고
    • Fractional Poisson bracket
    • K. Golmankhaneh Alireza Fractional Poisson bracket Turkish J. Phys. 32 2008 241 250
    • (2008) Turkish J. Phys. , vol.32 , pp. 241-250
    • Alireza, K.G.1
  • 36
    • 34047097242 scopus 로고    scopus 로고
    • Fractional embedding of differential operators and Lagrangian systems
    • J. Cresson Fractional embedding of differential operators and Lagrangian systems J. Math. Phys. 48 2007 033504
    • (2007) J. Math. Phys. , vol.48 , pp. 033504
    • Cresson, J.1
  • 37
    • 0036027310 scopus 로고    scopus 로고
    • Fractional sequential mechanics-models with symmetric fractional derivatives
    • K. Klimek Fractional sequential mechanics-models with symmetric fractional derivatives Czech. J. Phys. 52 2002 1247 1253
    • (2002) Czech. J. Phys. , vol.52 , pp. 1247-1253
    • Klimek, K.1
  • 38
    • 46249125645 scopus 로고    scopus 로고
    • Fractional conservation laws in optimal control theory
    • G.S.F. Frederico, and D.F.M. Torres Fractional conservation laws in optimal control theory Nonlinear Dynam. 53 3 2008 215 222
    • (2008) Nonlinear Dynam. , vol.53 , Issue.3 , pp. 215-222
    • Frederico, G.S.F.1    Torres, D.F.M.2
  • 39
    • 33745967716 scopus 로고    scopus 로고
    • Fractional calculus applications in signals and systems
    • DOI 10.1016/j.sigpro.2006.02.001, PII S0165168406000375, Fractional Calculus Applications in Signals and Systems
    • M.D. Ortigueira, and J.A. Tenreiro Machado Fractional calculus applications in signals and systems Signal Process. 86 10 2006 2503 2504 Elsevier (special issue) (Pubitemid 44055898)
    • (2006) Signal Processing , vol.86 , Issue.10 , pp. 2503-2504
    • Ortigueira, M.D.1    Machado, J.A.T.2
  • 40
    • 79960988286 scopus 로고    scopus 로고
    • Fractional differentiation and its applications
    • Sage Pub, (special issue)
    • M.D. Ortigueira, and J.A. Tenreiro Machado Fractional differentiation and its applications J. Vib. Control 14 910 2008 1253 Sage Pub, (special issue)
    • (2008) J. Vib. Control , vol.14 , Issue.910 , pp. 1253
    • Ortigueira, M.D.1    Tenreiro MacHado, J.A.2
  • 41
    • 47249105657 scopus 로고    scopus 로고
    • Discontinuous and fractional dynamical systems
    • 10.1115/1.2834905 (special issue)
    • M.D. Ortigueira, and J.A. Tenreiro Machado Discontinuous and fractional dynamical systems ASME J. Comput. Nonlinear Dynam. 3 2 2008 10.1115/1.2834905 (special issue)
    • (2008) ASME J. Comput. Nonlinear Dynam. , vol.3 , Issue.2
    • Ortigueira, M.D.1    Tenreiro MacHado, J.A.2
  • 42
    • 70349224466 scopus 로고    scopus 로고
    • Fractional-order Euler-Lagrange equations and formulation of Hamiltonian equations
    • A.E.H. Mohamed, and D. Baleanu Fractional-order Euler-Lagrange equations and formulation of Hamiltonian equations Nonlinear Dyn. 58 2009 385 391
    • (2009) Nonlinear Dyn. , vol.58 , pp. 385-391
    • Mohamed, A.E.H.1    Baleanu, D.2
  • 43
    • 44649143140 scopus 로고    scopus 로고
    • Fractional action like variational problems
    • R.A. El-Nabulsi, and D.F.M. Torres Fractional action like variational problems J. Math. Phys. 49 2008 053521
    • (2008) J. Math. Phys. , vol.49 , pp. 053521
    • El-Nabulsi, R.A.1    Torres, D.F.M.2
  • 44
    • 77952662203 scopus 로고    scopus 로고
    • Modifications at large distances from fractional and fractal arguments
    • R.A. El-Nabulsi Modifications at large distances from fractional and fractal arguments Fractals 18 2 2010 185 190
    • (2010) Fractals , vol.18 , Issue.2 , pp. 185-190
    • El-Nabulsi, R.A.1
  • 45
    • 67650832630 scopus 로고    scopus 로고
    • Black hole growth and accretion energy from fractional actionlike variational approach
    • R.A. El-Nabulsi Black hole growth and accretion energy from fractional actionlike variational approach Fizika B 17 3 2008 369 378
    • (2008) Fizika B , vol.17 , Issue.3 , pp. 369-378
    • El-Nabulsi, R.A.1
  • 46
    • 67649610631 scopus 로고    scopus 로고
    • On the fractional minimal length HeisenbergWeyl uncertainty relation from fractional Riccati generalized momentum operator
    • R.A. El-Nabulsi On the fractional minimal length HeisenbergWeyl uncertainty relation from fractional Riccati generalized momentum operator Chaos Solitons Fractals 42 2009 84 88
    • (2009) Chaos Solitons Fractals , vol.42 , pp. 84-88
    • El-Nabulsi, R.A.1
  • 47
    • 34547165802 scopus 로고    scopus 로고
    • A fractional action-like variational approach of some classical, quantum and geometrical dynamic
    • R.A. El-Nabulsi A fractional action-like variational approach of some classical, quantum and geometrical dynamic Int. J. Appl. Math. 17 3 2005 299 317
    • (2005) Int. J. Appl. Math. , vol.17 , Issue.3 , pp. 299-317
    • El-Nabulsi, R.A.1
  • 48
    • 44649143140 scopus 로고    scopus 로고
    • Fractional action like variational problems
    • R.A. El-Nabulsi, and D.F.M. Torres Fractional action like variational problems J. Math. Phys. 49 2008 053521
    • (2008) J. Math. Phys. , vol.49 , pp. 053521
    • El-Nabulsi, R.A.1    Torres, D.F.M.2
  • 49
    • 77957235666 scopus 로고    scopus 로고
    • Universal fractional Euler-Lagrange equation from a generalized fractional derivate operator
    • R.A. El-Nabulsi Universal fractional Euler-Lagrange equation from a generalized fractional derivate operator Cent. Eur. J. Phys. 9 1 2010 250 256
    • (2010) Cent. Eur. J. Phys. , vol.9 , Issue.1 , pp. 250-256
    • El-Nabulsi, R.A.1
  • 50
    • 40249091381 scopus 로고    scopus 로고
    • New Hamiltonian structure of the fractional C-KdV soliton equation hierarchy
    • F.J. Yu, and H.Q. Zhang New Hamiltonian structure of the fractional C-KdV soliton equation hierarchy Chaos Solitons Fractals 37 2008 688 697
    • (2008) Chaos Solitons Fractals , vol.37 , pp. 688-697
    • Yu, F.J.1    Zhang, H.Q.2
  • 51
    • 70149086250 scopus 로고    scopus 로고
    • Integrable coupling system of fractional soliton equation hierarchy
    • F.J. Yu Integrable coupling system of fractional soliton equation hierarchy Phys. Lett. A 373 2009 3730 3733
    • (2009) Phys. Lett. A , vol.373 , pp. 3730-3733
    • Yu, F.J.1
  • 52
    • 36649001872 scopus 로고    scopus 로고
    • Fractional zero curvature equation and generalized Hamiltonian structure of soliton equation hierarchy
    • F.J. Yu, and H.Q. Zhang Fractional zero curvature equation and generalized Hamiltonian structure of soliton equation hierarchy Internat. J. Theoret. Phys. 46 2007 3182 3192
    • (2007) Internat. J. Theoret. Phys. , vol.46 , pp. 3182-3192
    • Yu, F.J.1    Zhang, H.Q.2
  • 53
    • 0035532262 scopus 로고    scopus 로고
    • Fractional differential forms
    • S.K. Cottrill, and M. Naber Fractional differential forms J. Math. Phys. 42 2001 2203 2212
    • (2001) J. Math. Phys. , vol.42 , pp. 2203-2212
    • Cottrill, S.K.1    Naber, M.2
  • 54
    • 21244457230 scopus 로고    scopus 로고
    • Fractional generalization of gradient and Hamiltonian systems
    • E. Tarasov Fractional generalization of gradient and Hamiltonian systems J. Phys. A 38 2005 5929 5943
    • (2005) J. Phys. A , vol.38 , pp. 5929-5943
    • Tarasov, E.1
  • 56
    • 0002128448 scopus 로고
    • Fractional calculus
    • B. Ross Fractional calculus Math. Mag. 50 3 1977 115 122
    • (1977) Math. Mag. , vol.50 , Issue.3 , pp. 115-122
    • Ross, B.1
  • 57
    • 36549102254 scopus 로고
    • The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
    • G.T. Tu The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems J. Math. Phys. 30 2 1989 330 338
    • (1989) J. Math. Phys. , vol.30 , Issue.2 , pp. 330-338
    • Tu, G.T.1
  • 58
    • 36749109491 scopus 로고
    • An exact solution for a derivative nonlinear Schrödinger equation
    • D.J. Kaup, and A.C. Newell An exact solution for a derivative nonlinear Schrödinger equation J. Math. Phys. 19 1978 798 801
    • (1978) J. Math. Phys. , vol.19 , pp. 798-801
    • Kaup, D.J.1    Newell, A.C.2
  • 59
    • 23744468657 scopus 로고    scopus 로고
    • The multi-component Tu hierarchy of soliton equations and its multi-component integrable couplings system
    • DOI 10.1088/1009-1963/14/2/005
    • T.C. Xia, H. Wang, and Y.F. Zhang The multi-component Tu hierarchy of soliton equations and its multi-component integrable couplings system Chin. Phys. 14 2 2005 247 250 (Pubitemid 41237607)
    • (2005) Chinese Physics , vol.14 , Issue.2 , pp. 247-250
    • Xia, T.-C.1    Wang, H.2    Zhang, Y.-F.3
  • 60
    • 23244436758 scopus 로고    scopus 로고
    • A type of multi-component integrable hierarchy
    • Y.F. Zhang, and Y.S. Zhang A type of multi-component integrable hierarchy Chin. Phys. 13 8 2004 1183 1186
    • (2004) Chin. Phys. , vol.13 , Issue.8 , pp. 1183-1186
    • Zhang, Y.F.1    Zhang, Y.S.2
  • 61
    • 0034311570 scopus 로고    scopus 로고
    • Integrable evolution systems based on GerdjikovIvanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation
    • E.G. Fan Integrable evolution systems based on GerdjikovIvanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation J. Math. Phys. 41 11 2000 7769 7782
    • (2000) J. Math. Phys. , vol.41 , Issue.11 , pp. 7769-7782
    • Fan, E.G.1
  • 62
    • 17544403706 scopus 로고    scopus 로고
    • Enlarging spectral problems to construct integrable couplings of soliton equations
    • W.X. Ma Enlarging spectral problems to construct integrable couplings of soliton equations Phys. Lett. A 316 2003 72 76
    • (2003) Phys. Lett. A , vol.316 , pp. 72-76
    • Ma, W.X.1
  • 63
    • 20444481030 scopus 로고    scopus 로고
    • A multi-component matrix loop algebra and a unified expression of the multi-component AKNS hierarchy and the multi-component BPT hierarchy
    • Y.F. Zhang A multi-component matrix loop algebra and a unified expression of the multi-component AKNS hierarchy and the multi-component BPT hierarchy Phys. Lett. A 342 2005 82 89
    • (2005) Phys. Lett. A , vol.342 , pp. 82-89
    • Zhang, Y.F.1
  • 64
    • 4544345712 scopus 로고    scopus 로고
    • The multi-component coupled Burgers hierarchy of soliton equations and its multi-component integrable couplings system with two arbitrary functions
    • T.C. Xia, F.J. Yu, and Y. Zhang The multi-component coupled Burgers hierarchy of soliton equations and its multi-component integrable couplings system with two arbitrary functions Physica A 343 2004 238 246
    • (2004) Physica A , vol.343 , pp. 238-246
    • Xia, T.C.1    Yu, F.J.2    Zhang, Y.3
  • 65
    • 24344496561 scopus 로고    scopus 로고
    • The multi-component TD hierarchy and its multi-component integrable coupling system with five arbitrary functions
    • F.J. Yu, T.C. Xia, and H.Q. Zhang The multi-component TD hierarchy and its multi-component integrable coupling system with five arbitrary functions Chaos Solitons Fractals 27 2006 1036 1041
    • (2006) Chaos Solitons Fractals , vol.27 , pp. 1036-1041
    • Yu, F.J.1    Xia, T.C.2    Zhang, H.Q.3


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