The dual action of fractional multi time Hamilton equations

International Journal of Theoretical Physics

Volumn 48, Issue 9, 2009, Pages 2558-2569

  Baleanu, Dumitru ^a,b   Golmankhaneh, Ali Khalili ^d   Golmankhaneh, Alireza Khalili ^c,d  

^a CANKAYA UNIVERSITY   (Turkey)

^b INSTITUTE OF SPACE SCIENCES   (Romania)

^c UNIVERSITY OF PUNE   (India)

^d ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Constant of fractional motion; Dual action; Riemann Liouville derivative and fractional Euler Lagrange equations

Indexed keywords

EID: 70349621376     PISSN: 00207748     EISSN: 15729575     Source Type: Journal    
DOI: 10.1007/s10773-009-0042-x     Document Type: Article

References (31)

1. Agrawal, O.P.: Formulation of Euler-Lagrange equations for fractional variational problems. J. Math. Anal. Appl. 272, 368-379 (2002)
2. Baleanu, D., Muslih, S.: Lagrangian, formulation of classical fields within Riemann-Liouville fractional derivatives. Phys. Scr. 72, 119-121 (2005)
3. Baleanu, D., Agrawal, O.P.: Fractional Hamilton formalism within Caputo's derivative. Czech. J. Phys. 56, 1087-1092 (2006)
4. Baleanu, D., Muslih, S., Tas, K.: Fractional Hamiltonian analysis of higher order derivatives systems. J. Math. Phys. 47, 103503 (2006)
5. Baleanu, D., Golmankhaneh Alireza, K., Golmankhaneh Ali, K.: Fractional Nambu mechanics. Int. J. Theor. Phys. 48, 1044 (2009)
6. Constantina, U., Iulian, D.: Periodical solutions of multi time Hamilton equations. Anal. Univ. Bucuresti 55, 179-188 (2005)
7. De Donder, T.: Theorie invariative du des variations (1935)
8. Gorenflo, R., Mainardi, F.: Fractional Calculus: Integral and Differential Equations of Fractional Orders, Fractals and Fractional Calculus in Continuum Mechanics. Springer Verlag, New York (1997)
9. Frederico, G.S.F., Torres, D.F.M.: A formulation of Noether's theorem for fractional Problems of calculus of variations. J. Math. Anal. Appl. 334, 834-846 (2007)
10. Hilfer, R.: Application of Fractional Calculus in Physics. World Scientific, Singapore (2000)
11. Kilbas, A.A., Srivastava, H.H., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
12. Klimek, K.: Fractional sequential mechanics-models with symmetric fractional derivative. Czech. J. Phys. E 51, 1348-1354 (2001)
13. Klimek, K.: Lagrangean and Hamiltonian fractional sequential mechanics. Czech. J. Phys. E 52, 1247-1253 (2002)
14. Laskin, N.: Fractional quantum mechanics. Phys. Rev. E 62, 3135-3145 (2000)
15. Miller, K.S., Ross, B.: An Introduction to the Fractional Integrals and Derivatives-Theory and Application. Wiley, New York (1993)
16. Muslih, S., Baleanu, D.: Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives. J. Math. Anal. Appl. 304, 599-606 (2005)
17. Oldham, K.B., Spanier, J.: The Fractional Calculus. Academic Press, New York (1974)
18. Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1999)
19. Rabei, E.M., Nawafleh, K.I., Hiijawi, R.S., Muslih, S.I., Baleanu, D.: The Hamilton formalism with fractional derivatives. J. Math. Anal. Appl. 327, 891-897 (2007)
20. Rabei, E.M., Almayteh, I., Muslih, S.I., Baleanu, D.: Hamilton-Jaccobi formulation of systems with Caputo's fractional derivative. Phys. Scr. 77, 015101 (2007)
21. Rabei, E., Tarawneh, D.M., Muslih, S.I., Baleanu, D.: Heisenberg's equations of motio with fractional derivatives. J. Vib. Control 13, 1239-1247 (2007)
22. Riewe, F.: Nonconservative Lagrangian and Hamiltonian mechanics. Phys. Rev. E 53, 1890-1899 (1996)
23. Riewe, F.: Mechanics with fractional derivatives. Phys. Rev. E 55, 3581-3592 (1997)
24. Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives Theory and Applications. Gordon and Breach, New York (1993)
25. Tarasov, V.E.: Fractional variation for dynamical systems: Hamilton and Lagrange approaches. J. Phys. 39(26), 8409-8425 (2006)
26. Tarasov, V.E.: Fractional statistical mechanics. Chaos 16, 033108-033115 (2006)
27. Tarasov, V.E., Zaslavsky, G.M.: Fractional Ginzburg-Landau equation for fractal media. Physica A 354 (2005)
28. Udriste, C.: Fram integral to manifold and metrics to potential maps Atti del'Academia Peloritana dei Pericolanti, Class 1 di Scienze Fis. Mat. e Nat., vol. LXXXI-LXXXII, C1A0401008 (2003-2004)
29. West, B.J., Bologna, M., Grigolini, P.: Physics of Fractal Operators. Springer, New York (2003)
30. Zaslavsky, G.M.: Chaos, fractional kinetics, and anomalous transport. Phys. Rep. 371, 461-580 (2002)
31. Zaslavsky, G.M.: Hamiltonian Chaos and Fractional Dynamics. Oxford University Press, Oxford (2005)