메뉴 건너뛰기




Volumn 14, Issue 9-10, 2008, Pages 1301-1311

Nonconservative systems within fractional generalized derivatives

Author keywords

Fractional derivatives; Fractional Euler Lagrange equations; Fractional Hamiltonian; Fractional Lagrangian; Generalized derivatives; Nonconservative systems

Indexed keywords

CALCULATIONS; EQUATIONS OF MOTION; LAGRANGE MULTIPLIERS;

EID: 52349113178     PISSN: 10775463     EISSN: 17412986     Source Type: Journal    
DOI: 10.1177/1077546307087450     Document Type: Conference Paper
Times cited : (7)

References (36)
  • 1
    • 0141930931 scopus 로고    scopus 로고
    • A new Lagrangian and a new Lagrange equation of motion for fractionally damped systems
    • Agrawal, O.P., 2001, " A new Lagrangian and a new Lagrange equation of motion for fractionally damped systems, " ASME Journal of Applied Mechanics 68 (2). 339-341. 1.
    • (2001) ASME Journal of Applied Mechanics , vol.68 , Issue.2 , pp. 339-341
    • Agrawal, O.P.1
  • 2
    • 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, " Journal of Mathematical Analysis and Applications 272, 368-379.
    • (2002) Journal of Mathematical Analysis and Applications , vol.272 , pp. 368-379
    • Agrawal, O.P.1
  • 3
    • 15544379440 scopus 로고    scopus 로고
    • Application of fractional derivatives in thermal analysis of disk brakes
    • Agrawal, O.P., 2004, " Application of fractional derivatives in thermal analysis of disk brakes, " Nonlinear Dynamics 38 (1-4). 191-206.
    • (2004) Nonlinear Dynamics , vol.38 , Issue.1 , pp. 191-206
    • Agrawal, O.P.1
  • 5
    • 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 B52, 73-79.
    • (2004) Nuovo Cimento , vol.52 , pp. 73-79
    • Baleanu, D.1    Avkar, T.2
  • 6
    • 23344444772 scopus 로고    scopus 로고
    • Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives
    • Baleanu, D. and Muslih, S., 2005 a, " Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives, " Physica Scripta 72 (2-3). 119-121.
    • (2005) Physica Scripta , vol.72 , Issue.2 , pp. 119-121
    • Baleanu, D.1    Muslih, S.2
  • 7
    • 27844481567 scopus 로고    scopus 로고
    • About fractional supersymmetric quantum mechanics
    • Baleanu, D. and Muslih, S., 2005 b, " About fractional supersymmetric quantum mechanics, " Czechoslovak Journal of Physics 55 (9). 1063-1066.
    • (2005) Czechoslovak Journal of Physics , vol.55 , Issue.9 , pp. 1063-1066
    • Baleanu, D.1    Muslih, S.2
  • 8
    • 33750541076 scopus 로고    scopus 로고
    • Fractional Hamiltonian analysis of higher order derivatives systems
    • Baleanu, D., Muslih, S., and Tas, K., 2006, " Fractional Hamiltonian analysis of higher order derivatives systems, " Journal of Mathematical Physics 47 (10). 103503.1-103503.8.
    • (2006) Journal of Mathematical Physics , vol.47 , Issue.10 , pp. 1035031-1035038
    • Baleanu, D.1    Muslih, S.2    Tas, K.3
  • 9
    • 0001154626 scopus 로고
    • On dissipative systems and related variational principles
    • Bateman, H., 1931, " On dissipative systems and related variational principles, " Physical Review 38, 815-819.
    • (1931) Physical Review , vol.38 , pp. 815-819
    • Bateman, H.1
  • 11
    • 0022660581 scopus 로고    scopus 로고
    • On the fractional calculus model of viscoelastic behaviour
    • Blutzer, R.L. and Torvik, P.J., 1996, " On the fractional calculus model of viscoelastic behaviour, " Journal of Rheology 30, 133-135.
    • (1996) Journal of Rheology , vol.30 , pp. 133-135
    • Blutzer, R.L.1    Torvik, P.J.2
  • 15
    • 0002847893 scopus 로고    scopus 로고
    • Fractals and Fractional Calculus in Continuum Mechanics
    • CISM, Udine, Italy, pp.
    • Gorenflo, R. and Mainardi, F., 1997, " Integral and differential equations of fractional calculus, " in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, eds., CISM Courses and Lecture Notes, Vol. 378, CISM, Udine, Italy, pp. 223-276.
    • (1997) CISM Courses and Lecture Notes , vol.378 , pp. 223-276
    • Gorenflo, R.1    Mainardi, F.2
  • 17
    • 0035737230 scopus 로고    scopus 로고
    • Fractional sequential mechanics-models with symmetric fractional derivatives
    • Klimek, M., 2001, " Fractional sequential mechanics-models with symmetric fractional derivatives, " Czechoslovak Journal of Physics 51, 1348-1354.
    • (2001) Czechoslovak Journal of Physics , vol.51 , pp. 1348-1354
    • Klimek, M.1
  • 18
    • 0036027310 scopus 로고    scopus 로고
    • Lagrangean and Hamiltonian fractional sequential mechanics
    • Klimek, M., 2002, " Lagrangean and Hamiltonian fractional sequential mechanics, " Czechoslovak Journal of Physics 52, 1247-1253.
    • (2002) Czechoslovak Journal of Physics , vol.52 , pp. 1247-1253
    • Klimek, M.1
  • 20
    • 15544380308 scopus 로고    scopus 로고
    • Fractional trigonometry and the spiral functions
    • Lorenzo, C.F. and Hartley, T.T., 2004, " Fractional trigonometry and the spiral functions, " Nonlinear Dynamics 38 (1-2). 23-60.
    • (2004) Nonlinear Dynamics , vol.38 , Issue.1 , pp. 23-60
    • Lorenzo, C.F.1    Hartley, T.T.2
  • 21
    • 0030464353 scopus 로고    scopus 로고
    • Fractional relaxation-oscillation and fractional diffusion-wave phenomena," Chaos
    • Mainardi, F., 1996, " Fractional relaxation-oscillation and fractional diffusion-wave phenomena," Chaos, Solitons and Fractals 7, 1461-1477.
    • (1996) Solitons and Fractals , vol.7 , pp. 1461-1477
    • Mainardi, F.1
  • 22
    • 0001407424 scopus 로고    scopus 로고
    • The fundamental solution of the space-time fractional diffusion equation
    • Mainardi, F., Luchko, Y., and Pagnini, G., 2001, " The fundamental solution of the space-time fractional diffusion equation, " Fractional Calculus and Applied Analysis 4, 153-192.
    • (2001) Fractional Calculus and Applied Analysis , vol.4 , pp. 153-192
    • Mainardi, F.1    Luchko, Y.2    Pagnini, G.3
  • 24
    • 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, " Journal of Mathematical Analysis and Applications 304 (3). 599-606.
    • (2005) Journal of Mathematical Analysis and Applications , vol.304 , Issue.3 , pp. 599-606
    • Muslih, S.1    Baleanu, D.2
  • 27
    • 0000735791 scopus 로고    scopus 로고
    • Nonconservative Lagrangian and Hamiltonian mechanics
    • Riewe, F., 1996, " Nonconservative Lagrangian and Hamiltonian mechanics, " Physical Review 53, 1890-1899.
    • (1996) Physical Review , vol.53 , pp. 1890-1899
    • Riewe, F.1
  • 28
    • 4243530410 scopus 로고    scopus 로고
    • Mechanics with fractional derivatives
    • Riewe, F., 1997, " Mechanics with fractional derivatives, " Physical Review 55, 3581-3592.
    • (1997) Physical Review , vol.55 , pp. 3581-3592
    • Riewe, F.1
  • 30
    • 1842531858 scopus 로고    scopus 로고
    • Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation
    • Scalas, E., Gorenflo, R., and Mainardi, F., 2004, " Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation, " Physical Review E 69, 011107-011117.
    • (2004) Physical Review e , vol.69 , pp. 011107-011117
    • Scalas, E.1    Gorenflo, R.2    Mainardi, F.3
  • 33
    • 14844296496 scopus 로고    scopus 로고
    • A probabilistic interpretation of the fractional order differentiation
    • Tenreiro Machado, J.A., 2003, " A probabilistic interpretation of the fractional order differentiation, " Fractional Calculus and Applied Analysis 8, 73-80.
    • (2003) Fractional Calculus and Applied Analysis , vol.8 , pp. 73-80
    • Tenreiro MacHado, J.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.