메뉴 건너뛰기




Volumn 3, Issue 2, 2008, Pages

Fractional constrained systems and Caputo derivatives

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICAL SYSTEMS;

EID: 47249145244     PISSN: 15551423     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2833586     Document Type: Article
Times cited : (27)

References (45)
  • 9
    • 47249141215 scopus 로고    scopus 로고
    • F. Mainardi, A., 1997, Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics, Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, eds., Springer-Verlag, New York.
    • F. Mainardi, A., 1997, "Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics," Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, eds., Springer-Verlag, New York.
  • 10
    • 0142010055 scopus 로고    scopus 로고
    • On the Initial Conditions in Continuous-Time Fractional Linear Systems
    • Ortigueira, M. D., 2003, "On the Initial Conditions in Continuous-Time Fractional Linear Systems," Signal Process., 83(11), pp. 2301-2309.
    • (2003) Signal Process , vol.83 , Issue.11 , pp. 2301-2309
    • Ortigueira, M.D.1
  • 11
    • 0030651602 scopus 로고    scopus 로고
    • Analysis and Design of Fractional Order Digital Control Systems
    • Tenreiro Machado, J. A., 1997, "Analysis and Design of Fractional Order Digital Control Systems," Syst. Anal. Model. Simul., 27, pp. 107-122.
    • (1997) Syst. Anal. Model. Simul , vol.27 , pp. 107-122
    • Tenreiro Machado, J.A.1
  • 12
    • 0042494532 scopus 로고    scopus 로고
    • On a Riemann-Liouville Generalized Taylor'S Formula
    • Trujillo, J. J., 1999, "On a Riemann-Liouville Generalized Taylor'S Formula," J. Math. Anal. Appl., 231, pp. 255-265.
    • (1999) J. Math. Anal. Appl , vol.231 , pp. 255-265
    • Trujillo, J.J.1
  • 13
    • 0141921521 scopus 로고    scopus 로고
    • The Intrisic, Damping of the Fractional Oscillator
    • Tofighi, A., 2006, "The Intrisic, Damping of the Fractional Oscillator," Physica A, 329, pp. 29-34.
    • (2006) Physica A , vol.329 , pp. 29-34
    • Tofighi, A.1
  • 14
    • 1642641759 scopus 로고    scopus 로고
    • Fractional Laplacian Time-Space Models for Linear and Nonlinear Lossy Media Exhibiting Arbitrary Frequency Power-Law Dependency
    • Chen, W., and Holm, S., 2004, "Fractional Laplacian Time-Space Models for Linear and Nonlinear Lossy Media Exhibiting Arbitrary Frequency Power-Law Dependency," J. Acoust. Soc. Am., 115(4), pp. 1424-1430.
    • (2004) J. Acoust. Soc. Am , vol.115 , Issue.4 , pp. 1424-1430
    • Chen, W.1    Holm, S.2
  • 15
    • 2142704418 scopus 로고    scopus 로고
    • Fractional Dynamics, Cantorian Space-Time and the Gauge Hierarchy Problem
    • Goldfain, E., 2004, "Fractional Dynamics, Cantorian Space-Time and the Gauge Hierarchy Problem," Chaos, Solitons Fractals, 22(3), pp. 513-520.
    • (2004) Chaos, Solitons Fractals , vol.22 , Issue.3 , pp. 513-520
    • Goldfain, E.1
  • 16
    • 41149115805 scopus 로고    scopus 로고
    • da Graa Marcos, M., Duarte, F. B. M., and Tenreiro, Machado, J. A., 2007, Fractional Dynamics in the Trajectory Control of Redundant Manipulators, Commun. Nonlinear Sci, Numer. Simul., in press; doi: 10.1016/j.cnsns.2007.03.027.
    • da Graa Marcos, M., Duarte, F. B. M., and Tenreiro, Machado, J. A., 2007, Fractional Dynamics in the Trajectory Control of Redundant Manipulators," Commun. Nonlinear Sci, Numer. Simul., in press; doi: 10.1016/j.cnsns.2007.03.027.
  • 17
    • 77953520377 scopus 로고    scopus 로고
    • Formulation and a Numerical Scheme for Fractional Optimal Control Problems
    • Porto, Portugal, Jul. 19-21
    • Agrawal, O. P., 2006, "Formulation and a Numerical Scheme for Fractional Optimal Control Problems," Proceedings of the IFAC /FDA06, Porto, Portugal, Jul. 19-21.
    • (2006) Proceedings of the IFAC /FDA06
    • Agrawal, O.P.1
  • 18
    • 34748901185 scopus 로고    scopus 로고
    • A Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems
    • Agrawal, O. P., and Baleanu, D., 2007, "A Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems," J. Vib. Control, 13(9-10), pp. 1239-1247.
    • (2007) J. Vib. Control , vol.13 , Issue.9-10 , pp. 1239-1247
    • Agrawal, O.P.1    Baleanu, D.2
  • 19
    • 33646938767 scopus 로고    scopus 로고
    • Fractional Dynamics of Systems With Long-Range Interaction
    • Tarasov, V. E., and Zaslavsky, G. M., 2006, "Fractional Dynamics of Systems With Long-Range Interaction," Commun. Nonlinear Sci. Numer. Simul., 11(8), pp. 885-898.
    • (2006) Commun. Nonlinear Sci. Numer. Simul , vol.11 , Issue.8 , pp. 885-898
    • Tarasov, V.E.1    Zaslavsky, G.M.2
  • 20
    • 34249711357 scopus 로고    scopus 로고
    • Coupled Oscillators With Power-Law Interaction and Their Fractional Dynamics Analogues
    • Korabel, N., Zaslavsky, G. M., and Tarasov, V. E., 2007, "Coupled Oscillators With Power-Law Interaction and Their Fractional Dynamics Analogues," Commun. Nonlinear Sci. Numer. Simul., 12(8), pp. 1405-1417.
    • (2007) Commun. Nonlinear Sci. Numer. Simul , vol.12 , Issue.8 , pp. 1405-1417
    • Korabel, N.1    Zaslavsky, G.M.2    Tarasov, V.E.3
  • 21
    • 33750901303 scopus 로고    scopus 로고
    • A Numerical Scheme for the Solution of Multi-Order Fractional Differential Equations
    • Momani, S., 2006, "A Numerical Scheme for the Solution of Multi-Order Fractional Differential Equations," Appl. Math. Comput., 182, pp. 761-770.
    • (2006) Appl. Math. Comput , vol.182 , pp. 761-770
    • Momani, S.1
  • 22
    • 33750820240 scopus 로고    scopus 로고
    • A Domian Decomposition Methd for Solving Fractional Nonlinear Differential Equations
    • El-Wakil S. A., Elhanbaly, A., and Abdou, M. A., 2006, "A Domian Decomposition Methd for Solving Fractional Nonlinear Differential Equations," Appl. Math. Comput., 182, pp. 313-324.
    • (2006) Appl. Math. Comput , vol.182 , pp. 313-324
    • El-Wakil, S.A.1    Elhanbaly, A.2    Abdou, M.A.3
  • 23
    • 0000735791 scopus 로고    scopus 로고
    • Nonconservative Lagrangian and Hamiltonian Mechanics
    • Riewe, F., 1996, "Nonconservative Lagrangian and Hamiltonian Mechanics," Phys. Rev. E, 55, pp. 1890-1899.
    • (1996) Phys. Rev. E , vol.55 , pp. 1890-1899
    • Riewe, F.1
  • 24
    • 4243530410 scopus 로고    scopus 로고
    • Mechanics With Fractional Derivatives
    • Riewe, F, 1997, "Mechanics With Fractional Derivatives," Phys. Rev. E, 55, pp. 3581-3592.
    • (1997) Phys. Rev. E , vol.55 , pp. 3581-3592
    • Riewe, F.1
  • 25
    • 0036027310 scopus 로고    scopus 로고
    • Lagrangian and Hamiltonian Fractional Sequential Mechanics
    • Klimek, M., 2002, "Lagrangian and Hamiltonian Fractional Sequential Mechanics," Czech. J. Phys., 52, pp. 1247-1254.
    • (2002) Czech. J. Phys , vol.52 , pp. 1247-1254
    • Klimek, M.1
  • 26
    • 41149152515 scopus 로고    scopus 로고
    • Conservation Laws and Hamilton'S Equations for Systems With Long-Range Interaction and Memory
    • in press; doi: 10.1016/j.cnsns.2007.05.017
    • Tarasov, V. E., and Zaslavsky, G. M., 2007, "Conservation Laws and Hamilton'S Equations for Systems With Long-Range Interaction and Memory," Commun. Nonlinear Sci. Numer. Simul., in press; doi: 10.1016/j.cnsns.2007.05.017.
    • (2007) Commun. Nonlinear Sci. Numer. Simul
    • Tarasov, V.E.1    Zaslavsky, G.M.2
  • 27
    • 0001805106 scopus 로고    scopus 로고
    • Discrete-Time Fractional-Order Controllers
    • Tenreiro Machado, J. A., 2001, "Discrete-Time Fractional-Order Controllers," Fractional Calculus Appl. Anal., 4(1), pp. 47-68.
    • (2001) Fractional Calculus Appl. Anal , vol.4 , Issue.1 , pp. 47-68
    • Tenreiro Machado, J.A.1
  • 28
    • 0036701004 scopus 로고    scopus 로고
    • Formulation of Euler-Lagrange Equations for Fractional Variational Problems
    • Agrawal, O. P., 2002, "Formulation of Euler-Lagrange Equations for Fractional Variational Problems," J. Math. Anal. Appl., 272, pp. 368-379.
    • (2002) J. Math. Anal. Appl , vol.272 , pp. 368-379
    • Agrawal, O.P.1
  • 29
    • 4544250038 scopus 로고    scopus 로고
    • Time Fractional Schrödinger Equation
    • Naber, M., 2004, "Time Fractional Schrödinger Equation," J. Math. Phys., 45, pp. 3339-3352.
    • (2004) J. Math. Phys , vol.45 , pp. 3339-3352
    • Naber, M.1
  • 30
    • 4043144342 scopus 로고    scopus 로고
    • Probability Interpretation of the Integral of Fractional Order
    • Stanislavsky, A. A., 2005, "Probability Interpretation of the Integral of Fractional Order," Theor. Math. Phys., 138, pp. 418-431.
    • (2005) Theor. Math. Phys , vol.138 , pp. 418-431
    • Stanislavsky, A.A.1
  • 31
    • 0004681849 scopus 로고
    • The Fractional Integral and Its Physical Interpretation
    • Nigmatullin, R. R., 1992, "The Fractional Integral and Its Physical Interpretation," Theor. Math. Phys., 90, pp. 242-251.
    • (1992) Theor. Math. Phys , vol.90 , pp. 242-251
    • Nigmatullin, R.R.1
  • 32
    • 33746069046 scopus 로고    scopus 로고
    • Electromagnetic Fields on Fractals
    • Tarasov, V. E., 2006, "Electromagnetic Fields on Fractals," Mod. Phys. Lett. A, 12, pp. 1587-1600.
    • (2006) Mod. Phys. Lett. A , vol.12 , pp. 1587-1600
    • Tarasov, V.E.1
  • 33
    • 67650793831 scopus 로고    scopus 로고
    • Differential Geometry and Modern Cosmology With Fractionaly Differentiated Lagrangian Function and Fractional Decaying Force Term
    • El-Nabulusi, R. A., 2007, "Differential Geometry and Modern Cosmology With Fractionaly Differentiated Lagrangian Function and Fractional Decaying Force Term," Rom. J. Phys., 52, pp. 441-450.
    • (2007) Rom. J. Phys , vol.52 , pp. 441-450
    • El-Nabulusi, R.A.1
  • 34
    • 33746876366 scopus 로고    scopus 로고
    • Fractional Variational Calculus and the Transversality Conditions
    • Agrawal, O. P., 2006, "Fractional Variational Calculus and the Transversality Conditions," J. Phys. A, 39, pp. 10375-10384.
    • (2006) J. Phys. A , vol.39 , pp. 10375-10384
    • Agrawal, O.P.1
  • 35
    • 14844283120 scopus 로고    scopus 로고
    • Hamiltonian Formulation of Systems With Linear Velocities Within Riemann-Liouville Fractional Derivatives
    • Muslih, S., and Baleanu, D., 2005, "Hamiltonian Formulation of Systems With Linear Velocities Within Riemann-Liouville Fractional Derivatives," J. Math. Anal. Appl., 304(3), pp. 599-603.
    • (2005) J. Math. Anal. Appl , vol.304 , Issue.3 , pp. 599-603
    • Muslih, S.1    Baleanu, D.2
  • 36
    • 33745870156 scopus 로고    scopus 로고
    • Fractional Hamiltoian Analysis of Irregular Systems
    • Baleanu, D., 2006, "Fractional Hamiltoian Analysis of Irregular Systems," Signal Process., 86(10), pp. 2632-2636.
    • (2006) Signal Process , vol.86 , Issue.10 , pp. 2632-2636
    • Baleanu, D.1
  • 37
    • 21644464298 scopus 로고    scopus 로고
    • Formulation of Hamiltonian Equations for Fractional Variational Problems
    • Baleanu, D., and Muslih, S. I., 2005, "Formulation of Hamiltonian Equations for Fractional Variational Problems," Czech. J. Phys., 55(6), pp. 633-642.
    • (2005) Czech. J. Phys , vol.55 , Issue.6 , pp. 633-642
    • Baleanu, D.1    Muslih, S.I.2
  • 38
    • 23344444772 scopus 로고    scopus 로고
    • Lagrangian Formulation of Classical Fields Within Riemann-Liouville Fractional Derivatives
    • Baleanu, D., and Muslih, S. I., 2005, "Lagrangian Formulation of Classical Fields Within Riemann-Liouville Fractional Derivatives," Phys. Ser., 72(2-3), pp. 119-121.
    • (2005) Phys. Ser , vol.72 , Issue.2-3 , pp. 119-121
    • Baleanu, D.1    Muslih, S.I.2
  • 39
    • 4043139312 scopus 로고    scopus 로고
    • Lagrangians With Linear Velocities Within Riemann-Liouville Fractional Derivatives
    • Baleanu, D., and Avkar, T., 2004, "Lagrangians With Linear Velocities Within Riemann-Liouville Fractional Derivatives," Nuovo Cimento B, 119, pp. 73-79.
    • (2004) Nuovo Cimento B , vol.119 , pp. 73-79
    • Baleanu, D.1    Avkar, T.2
  • 40
    • 33750541076 scopus 로고    scopus 로고
    • Fractional Hamiltonian Analysis of Higher Order Derivatives Systems
    • Baleanu, D., Muslih, S. I., and Tas, K., 2006, "Fractional Hamiltonian Analysis of Higher Order Derivatives Systems," J. Math. Phys., 47(10), pp. 1-10.
    • (2006) J. Math. Phys , vol.47 , Issue.10 , pp. 1-10
    • Baleanu, D.1    Muslih, S.I.2    Tas, K.3
  • 42
    • 33845669957 scopus 로고    scopus 로고
    • Fractional Hamilton Formalism Within Caputo's Derivative
    • Baleanu, D., and Agrawal, O. P., 2006, "Fractional Hamilton Formalism Within Caputo's Derivative," Czech. J. Phys., 56(10-11), pp, 1087-1092.
    • (2006) Czech. J. Phys , vol.56 , Issue.10-11 , pp. 1087-1092
    • Baleanu, D.1    Agrawal, O.P.2
  • 43
    • 33947372609 scopus 로고    scopus 로고
    • The Fractional Symmetric Rigid Rotor
    • Hermann, R., 2007, "The Fractional Symmetric Rigid Rotor," J. Phys. G, 34, pp. 607-625.
    • (2007) J. Phys. G , vol.34 , pp. 607-625
    • Hermann, R.1
  • 45
    • 33845306847 scopus 로고    scopus 로고
    • Lagrangian Mechanics of Fractional Order, Hamilton-Jacobi Fractional PDE and Taylor's Series of Nondifferentiable, Functions
    • Jumarie, G., 2007, "Lagrangian Mechanics of Fractional Order, Hamilton-Jacobi Fractional PDE and Taylor's Series of Nondifferentiable, Functions," Chaos, Solitons Fractals, 32, pp. 969-987.
    • (2007) Chaos, Solitons Fractals , vol.32 , pp. 969-987
    • Jumarie, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.