Fractional variational problems from extended exponentially fractional integral

Applied Mathematics and Computation

Volumn 217, Issue 22, 2011, Pages 9492-9496

  Rami, El Nabulsi Ahmad ^a  

^a NEIJIANG NORMAL UNIVERSITY   (China)

Author keywords

Extended exponentially fractional integral; Fractional action like variational approach; Lagrangian and Hamiltonian formalism

Indexed keywords

FRACTIONAL ACTION-LIKE VARIATIONAL APPROACH; FRACTIONAL INTEGRALS; HAMILTONIAN FORMULATIONS; LAGRANGIAN; LAGRANGIAN AND HAMILTONIAN FORMALISM; VARIATIONAL PROBLEMS;

HAMILTONIANS; LAGRANGE MULTIPLIERS;

VARIATIONAL TECHNIQUES;

EID: 79957454704     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.04.007     Document Type: Article

References (48)

1. J. Sabatier, O.P. Agrawal, and J.A. Tenreiro Machado Advance in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering 2007 Springer
2. D. Baleanu, B. Guvenc Ziya, and J.A. Tenreiro New Trends in Nanotechnology and Fractional Calculus Applications 2009 Springer
3. R. Hilfer Application of Fractional Calculus in Physics 2000 World Scientific Singapore
4. R. Goreno, and F. Mainardi Fractional Calculus: Integral and Differential Equations of Fractional Orders Fractals and Fractional Calculus in Continuum Mechanics 1997 Springer Verlag New York
5. A.A. Kilbas, H.H. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations 2006 Elsevier The Netherlands
6. K.B. Oldham, and J. Spanier The Fractional Calculus 1974 Academic New York
7. K.S. Miller, and B. Ross An Introduction to the Fractional Integrals and Derivatives-Theory and Application 1993 Wiley New York
8. I. Podlubny Fractional Differential Equations 1999 Academic New York
9. S.G. Samko, A.A. Kilbas, and O.I. Marichev Fractional Integrals and Derivatives Theory and Applications 1993 Gordon and Breach New York
10. B.J. West, M. Bologna, P. Grigolini, Physics of Fractal Operators, New York, 2003.
11. G.M. Zaslavsky Hamiltonian Chaos and Fractional Dynamics 2005 Oxford University Press
12. R.A. El-Nabulsi Application of the fractional problem of the calculus of variations and the fractional path integral to stochastic modeling Fizika A 19 1 2010 11 30
13. R.A. El-Nabulsi Fractional dynamics, fractional weak bosons masses and physics beyond the standard model Chaos, Solitons Fractals 41 2009 2262 2270
14. R.A. El-Nabulsi On the fractional minimal length Heisenberg-Weyl uncertainty relation from fractional Riccati generalized momentum operator Chaos, Solitons Fractals 42 2009 84 88
15. F. Riewe Nonconservative Lagrangian and Hamiltonian mechanics Phys. Rev. E 53 1996 1890 1899 (Pubitemid 126583833)
16. R.P. Agarwal Yong Zhou and Yunyun He, Existence of fractional neutral functional differential equations Comput. Math. Appl. 59 2010 1095 1100
17. O.P. Agrawal Formulation of Euler-Lagrange equations for fractional variational problems J. Math. Anal. Appl. 272 2002 368 379
18. O.P. Agrawal Fractional variational calculus and the transversality conditions J. Phys. A. Math. Gen. 39 2006 10375 10384 (Pubitemid 44183559)
19. T.M. Atanackovic, and B. Stankovic An expansion formula for fractional derivatives Fract. Calc. Appl. Anal. 7 2004 365 378
20. D. Baleanu, and S. Muslih Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives Phys. Scr. 72 2005 119 121 (Pubitemid 41101668)
21. D. Baleanu, and O.P. Agrawal Fractional Hamilton formalism within Caputo's derivative Czech. J. Phys. 56 2006 1087 1092 (Pubitemid 44951048)
22. D. Baleanu, S. Muslih, and K. Tas Fractional Hamiltonian analysis of higher order derivatives systems J. Math. Phys. 47 2006 103503 103523
23. 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
24. G.S.F. Frederico, and D.F.M. Torres Constants of motion for fractional action- like variational problems Int. J. Appl. Math. 19 1 2005 97 104
25. G.S.F. Frederico, and D.F.M. Torres Conservation laws for invariant functionals containing compositions Appl. Anal. 86 9 2007 1117 1126
26. G.S.F. Frederico, and D.F.M. Torres A formulation of Noether's theorem for fractional problems of the calculus of variations Int. Math. Forum 3 9 2008 479 493
27. G.S.F. Frederico, and D.F.M. Torres Fractional conservation laws in optimal control theory Nonlinear Dyn. 53 3 2008 215 222
28. R.A. El-Nabulsi Some geometrical aspects of nonconservative autonomous Hamiltonian dynamical systems Int. J. Appl. Math. Stat. 5 2006 50 61 S06
29. R.A. El-Nabulsi Fractional quantum Euler-Cauchy equation in the Schrodinger picture, complexified harmonic oscillators and emergence of complexified Lagrangian and Hamiltonian dynamics Mod. Phys. Lett. B 23 28 2009 3369 3386
30. R.A. El-Nabulsi, and D.F.M. Torres Fractional action like variational problems J. Math. Phys. 49 2008 053429 053521
31. R.A. El-Nabulsi Generalized fractal space from Erdelyi-Kober fractional integral Fizika A 19 3 2010 125 132
32. R.A. El-Nabulsi Higher-order fractional field equations in (0 + 1) dimensions and physics beyond the standard model Fizika A 19 2 2010 55 72
33. R.A. El-Nabulsi The fractional calculus of variations from extended Erdelyi-Kober operator Int. J. Mod. Phys. B 23 16 2009 3349 3361
34. R.A. El-Nabulsi Universal fractional Euler-Lagrange equation from a generalized fractional derivate operator Central Europ. J. Phys. 9 1 2010 250 256
35. R.A. El-Nabulsi Fractional field theories from multidimensional fractional variational problems Int. J. Geom. Meth. Mod. Phys. 5 6 2008 863 892
36. R.A. El-Nabulsi, and D.F.M. Torres Necessary optimality condition for fractional action-like variational approach with-Liouville derivatives of order (alfa, betta) Math. Meth. Appl. Sci. 30 15 2007 1931 1939 (Pubitemid 47395843)
37. R.A. El-Nabulsi A fractional approach to nonconservative Lagrangian dynamical systems Fizika A 14 4 2005 289 298
38. R.A. El-Nabulsi A fractional action-like variational approach of some classical, quantum and geometrical dynamics Int. J. Appl. Math. 17 3 2005 299 317
39. G.S.F. Frederico, and D.F.M. Torres Fractional Noether's theorem in the Riesz-Caputo sense Appl. Math. Comput. 217 3 2010 1023 1033
40. R.A. El-Nabulsi Modifications at large distances from fractional and fractal arguments FRACTALS 18 2 2010 185 190
41. R.A. El-Nabulsi Fractional quantum field theory on multifractals sets American J. Eng. Appl. Sci. 4 1 2010 133 141
42. T.P. Cheng, and L.F. Li Gauge Theory of Elementary Particle Physics 1983 Oxford University Press
43. P. Frampton Gauge Field Theories third ed. 2008 Wiley VCH
44. R. Almeida, and D.F.M. Torres Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives Commun. Nonlinear Sci. Numer. Simul. 16 3 2011 1490 1500
45. A.B. Malinowska, and D.F.M. Torres The generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative Comput. Math. Appl. 59 9 2010 3110 3116
46. N.R.O. Bastos, R.A.C. Ferreira, and D.F.M. Torres Discrete-time fractional variational problems Signal Process. 91 3 2011 513 524
47. J. Cresson Inverse problem of fractional calculus of variations for partial differential equations Commun. Nonlinear Sci. Numer. Simul. 15 4 2010 987 996
48. R.A. El-Nabulsi, Extended fractional calculus of variations, complexified geodesics and Wong's fractional equation on complex place and Lie algebroids, Annales Universitatis Mariae Curie -Skłodowska, Sectio A (Mathematica), in press.