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Volumn 58, Issue 1-2, 2009, Pages 385-391

Fractional-order Euler-Lagrange equations and formulation of Hamiltonian equations

Author keywords

Fractional calculus of variations; Fractional derivative; Fractional Hamiltonian equations; Fractional integral

Indexed keywords

EULER-LAGRANGE EQUATIONS; FRACTIONAL CALCULUS OF VARIATIONS; FRACTIONAL DERIVATIVE; FRACTIONAL DERIVATIVES; FRACTIONAL HAMILTONIAN EQUATIONS; FRACTIONAL INTEGRAL; FRACTIONAL INTEGRALS; FRACTIONAL ORDER; HAMILTONIAN EQUATIONS; HAMILTONIAN FORMULATIONS; ILLUSTRATIVE EXAMPLES; TRANSVERSALITY CONDITIONS; VARIATIONAL PROBLEMS;

EID: 70349224466     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-009-9486-z     Document Type: Article
Times cited : (79)

References (30)
  • 1
    • 0141930931 scopus 로고    scopus 로고
    • A new Lagrangian and a new Lagrange equation of motion for fractionally damped systems
    • 1110.74310 10.1115/1.1352017
    • O.P. Agrawal 2001 A new Lagrangian and a new Lagrange equation of motion for fractionally damped systems J. Appl. Mech. 68 339 341 1110.74310 10.1115/1.1352017
    • (2001) J. Appl. Mech. , vol.68 , pp. 339-341
    • Agrawal, O.P.1
  • 2
    • 0036701004 scopus 로고    scopus 로고
    • Formulation of Euler-Lagrange equations for fractional variational problems
    • 1070.49013 10.1016/S0022-247X(02)00180-4 1930721
    • O.P. Agrawal 2002 Formulation of Euler-Lagrange equations for fractional variational problems J. Math. Anal. Appl. 272 368 379 1070.49013 10.1016/S0022-247X(02)00180-4 1930721
    • (2002) J. Math. Anal. Appl. , vol.272 , pp. 368-379
    • Agrawal, O.P.1
  • 3
    • 33746876366 scopus 로고    scopus 로고
    • Fractional variational calculus and the transversality conditions
    • DOI 10.1088/0305-4470/39/33/008, PII S0305447006218080, 008
    • O.P. Agrawal 2006 Fractional variational calculus and the transversality conditions J. Phys. A, Math. Gen. 39 10375 10384 1097.49021 10.1088/0305-4470/ 39/33/008 (Pubitemid 44183559)
    • (2006) Journal of Physics A: Mathematical and General , vol.39 , Issue.33 , pp. 10375-10384
    • Agrawal, O.P.1
  • 4
    • 34548226960 scopus 로고    scopus 로고
    • A general finite element formulation for fractional variational problems
    • 1123.65059 10.1016/j.jmaa.2007.03.105 2356049
    • O.P. Agrawal 2008 A general finite element formulation for fractional variational problems J. Math. Anal. Appl. 337 1 12 1123.65059 10.1016/j.jmaa.2007.03.105 2356049
    • (2008) J. Math. Anal. Appl. , vol.337 , pp. 1-12
    • Agrawal, O.P.1
  • 6
    • 33845669957 scopus 로고    scopus 로고
    • Fractional Hamilton formalism within Caputo's derivative
    • DOI 10.1007/s10582-006-0406-x
    • D. Baleanu O.P. Agrawal 2006 Fractional Hamilton formalism within Caputo's derivative Czech. J. Phys. 56 10-11 1087 1092 10.1007/s10582-006-0406-x 2282282 (Pubitemid 44951048)
    • (2006) Czechoslovak Journal of Physics , vol.56 , Issue.10-11 , pp. 1087-1092
    • Baleanu, D.1    Agrawal, O.P.2
  • 7
    • 4043139312 scopus 로고    scopus 로고
    • Lagrangians with linear velocities within Riemann-Liouville fractional derivatives
    • D. Baleanu T. Avkar 2004 Lagrangians with linear velocities within Riemann-Liouville fractional derivatives Nuovo Cim. B 119 73 79
    • (2004) Nuovo Cim. B , vol.119 , pp. 73-79
    • Baleanu, D.1    Avkar, T.2
  • 9
    • 34548580114 scopus 로고    scopus 로고
    • A fractional approach of nonconservative Lagrangian dynamics
    • R.A. El-Nabulsi 2005 A fractional approach of nonconservative Lagrangian dynamics Fizika A 14 4 289 298
    • (2005) Fizika A , vol.14 , Issue.4 , pp. 289-298
    • El-Nabulsi, R.A.1
  • 10
    • 34547165802 scopus 로고    scopus 로고
    • A fractional action-like variational approach of some classical, quantum and geometrical dynamics
    • 1137.70349 2191270
    • R.A. El-Nabulsi 2005 A fractional action-like variational approach of some classical, quantum and geometrical dynamics Int. J. Appl. Math. 17 3 299 317 1137.70349 2191270
    • (2005) Int. J. Appl. Math. , vol.17 , Issue.3 , pp. 299-317
    • El-Nabulsi, R.A.1
  • 11
    • 34548583736 scopus 로고    scopus 로고
    • Necessary optimality conditions for fractional action-like integrals of variational calculus with Riemann-Liouville derivatives of order (α, β)
    • DOI 10.1002/mma.879
    • R.A. El-Nabulsi D.F.M. Torres 2007 Necessary optimality conditions for fractional action-like integrals of variational calculus with Riemann-Liouville derivatives of order (α, β) Math. Methods Appl. Sci. 30 15 1931 1939 05224078 10.1002/mma.879 2349759 (Pubitemid 47395843)
    • (2007) Mathematical Methods in the Applied Sciences , vol.30 , Issue.15 , pp. 1931-1939
    • El-Nabulsi, R.A.1    Torres, D.F.M.2
  • 13
    • 77956684069 scopus 로고    scopus 로고
    • Theory and Applications of Fractional Differential Equations
    • Elsevier Amsterdam 1092.45003 10.1016/S0304-0208(06)80001-0
    • Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematical Studies, vol. 204. Elsevier, Amsterdam (2006)
    • (2006) North-Holland Mathematical Studies , vol.204
    • Kilbas, A.A.1    Srivastava, H.M.2    Trujillo, J.J.3
  • 14
    • 0035737230 scopus 로고    scopus 로고
    • Fractional sequential mechanics - Models with symmetric fractional derivative
    • DOI 10.1023/A:1013378221617
    • M. Klimek 2001 Fractional sequential mechanics-models with symmetric fractional derivative Czech. J. Phys. 51 1348 1354 1064.70507 10.1023/A:1013378221617 1917624 (Pubitemid 33576189)
    • (2001) Czechoslovak Journal of Physics , vol.51 , Issue.12 , pp. 1348-1354
    • Klimek, M.1
  • 15
    • 0037047631 scopus 로고    scopus 로고
    • Stationarity-conservation laws for fractional differential equations with variable coefficients
    • DOI 10.1088/0305-4470/35/31/311, PII S0305447002353848
    • M. Klimek 2002 Stationary conservation laws for fractional differential equations with variable coefficients J. Phys. A, Math. Gen. 35 6675 6693 1039.35005 10.1088/0305-4470/35/31/311 1928856 (Pubitemid 37049354)
    • (2002) Journal of Physics A: Mathematical and General , vol.35 , Issue.31 , pp. 6675-6693
    • Klimek, M.1
  • 16
    • 15544380308 scopus 로고    scopus 로고
    • Fractional trigonometry and the spiral functions
    • DOI 10.1007/s11071-004-3745-9
    • C.F. Lorenzo T.T. Hartley 2004 Fractional trigonometry and the spiral functions Nonlinear Dyn. 38 1-4 23 60 1094.26004 10.1007/s11071-004-3745-9 2112167 (Pubitemid 40400606)
    • (2004) Nonlinear Dynamics , vol.38 , Issue.1-4 , pp. 23-60
    • Lorenzo, C.F.1    Hartley, T.T.2
  • 17
    • 52549095901 scopus 로고    scopus 로고
    • Fractional control of heat diffusion systems
    • 10.1007/s11071-007-9322-2 2464537
    • I.S. Jesus J.A.T. Machado 2008 Fractional control of heat diffusion systems Nonlinear Dyn. 54 3 263 282 10.1007/s11071-007-9322-2 2464537
    • (2008) Nonlinear Dyn. , vol.54 , Issue.3 , pp. 263-282
    • Jesus, I.S.1    MacHado, J.A.T.2
  • 18
    • 3042776917 scopus 로고    scopus 로고
    • Fractional calculus in bioengineering
    • 10.1615/CritRevBiomedEng.v32.10
    • R.L. Magin 2004 Fractional calculus in bioengineering Parts 1-3, Crit. Rev. Biomed. Eng. 32 1 1 377 10.1615/CritRevBiomedEng.v32.10
    • (2004) Parts 1-3, Crit. Rev. Biomed. Eng. , vol.32 , Issue.1 , pp. 1-377
    • Magin, R.L.1
  • 20
    • 14844283120 scopus 로고    scopus 로고
    • Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives
    • DOI 10.1016/j.jmaa.2004.09.043, PII S0022247X04008005
    • S.I. Muslih D. Baleanu 2005 Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives J. Math. Anal. Appl. 304 599 606 1149.70320 10.1016/j.jmaa.2004.09.043 2126553 (Pubitemid 40350289)
    • (2005) Journal of Mathematical Analysis and Applications , vol.304 , Issue.2 , pp. 599-606
    • Muslih, S.I.1    Baleanu, D.2
  • 21
    • 21644464298 scopus 로고    scopus 로고
    • Formulation of Hamiltonian equations for fractional variational problems
    • DOI 10.1007/s10582-005-0067-1
    • S.I. Muslih D. Baleanu 2005 Formulation of Hamiltonian equations for fractional variational problems Czech. J. Phys. 55 633 642 10.1007/s10582-005- 0067-1 2169356 (Pubitemid 40937431)
    • (2005) Czechoslovak Journal of Physics , vol.55 , Issue.6 , pp. 633-642
    • Muslih, S.I.1    Baleanu, D.2
  • 22
    • 52349114814 scopus 로고    scopus 로고
    • Fractional central differences and derivatives
    • 10.1177/1077546307087453 2463063
    • M.D. Ortigueira 2008 Fractional central differences and derivatives J. Vib. Control 14 9-10 1255 1266 10.1177/1077546307087453 2463063
    • (2008) J. Vib. Control , vol.14 , Issue.910 , pp. 1255-1266
    • Ortigueira, M.D.1
  • 24
    • 0000735791 scopus 로고    scopus 로고
    • Nonconservative Lagrangian and Hamiltonian mechanics
    • 10.1103/PhysRevE.53.1890 1401316
    • F. Riewe 1996 Nonconservative Lagrangian and Hamiltonian mechanics Phys. Rev. E 53 2 1890 1899 10.1103/PhysRevE.53.1890 1401316
    • (1996) Phys. Rev. e , vol.53 , Issue.2 , pp. 1890-1899
    • Riewe, F.1
  • 25
    • 4243530410 scopus 로고    scopus 로고
    • Mechanics with fractional derivatives
    • 10.1103/PhysRevE.55.3581 1438729
    • F. Riewe 1997 Mechanics with fractional derivatives Phys. Rev. E 55 3 3582 3592 10.1103/PhysRevE.55.3581 1438729
    • (1997) Phys. Rev. e , vol.55 , Issue.3 , pp. 3582-3592
    • Riewe, F.1
  • 26
    • 52349114298 scopus 로고    scopus 로고
    • A fractional adaptation scheme for lateral control of an AGV
    • 10.1177/1077546307087434 2463075
    • J.I. Suarez B.M. Vinagre Y.Q. Chen 2008 A fractional adaptation scheme for lateral control of an AGV J. Vib. Control 14 9-10 1499 1511 10.1177/1077546307087434 2463075
    • (2008) J. Vib. Control , vol.14 , Issue.910 , pp. 1499-1511
    • Suarez, J.I.1    Vinagre, B.M.2    Chen, Y.Q.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.