Fractional variational principles in action

Physica Scripta T

Volumn T136, Issue , 2009, Pages

  Baleanu, Dumitru ^a,b  

^a CANKAYA UNIVERSITY   (Turkey)

^b INSTITUTE OF SPACE SCIENCES   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

FRACTIONAL CALCULUS; FRACTIONAL VARIATIONAL PRINCIPLES; LAGRANGE AND HAMILTON EQUATIONS; POTENTIAL APPLICATIONS; SCIENCE AND ENGINEERING;

EULER EQUATIONS; VARIATIONAL TECHNIQUES;

DIFFERENTIATION (CALCULUS);

EID: 77952842666     PISSN: 02811847     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1088/0031-8949/2009/T136/014006     Document Type: Conference Paper

References (59)

1. Oldham K B and Spanier J 1974 The Fractional Calculus (New York: Academic)
2. Miller K S and Ross B 1993 An Introduction to the Fractional Integrals and Derivatives-Theory and Application (New York: Wiley)
3. Samko S G, Kilbas A A and Marichev O I F 1993 Fractional Integrals and Derivatives-Theory and Applications (Linghorne, PA: Gordon and Breach)
4. Hilfer R 2000 Applications of Fractional Calculus in Physics (Singapore: World Scientific)
5. Podlubny I 1999 Fractional Differential Equations (New York: Academic)
6. Zaslavsky G M 2005 Hamiltonian Chaos and Fractional Dynamics (Oxford: Oxford University Press)
7. Kilbas A A, Srivastava H M and Trujillo J J 2006 Theory and Applications of Fractional Differential Equations (Amsterdam: Elsevier)
8. West B J, Bologna M and Grigolini P 2003 Physics of Fractal Operators (New York: Springer)
9. Metzler R, Schick W, Kilian H G T and Nonennmacher F 1995 J. Chem. Phys. 103 7180
10. Magin R L 2006 Fractional Calculus in Bioengineering (Connecticut: Begell House Publication)
11. Sabatier J, Agrawal O P and Tenreiro Machado J A (eds) 2007 Advances in Fractional Calculus. Theoretical Developments and Applications in Physics and Engineering (Dordrecht: Springer)
12. Glöcke W G and Nonnenmacher T F 1991 Macromolecules 24 6426
13. Glöcke W G and Nonnenmacher T F 1995 Biophys. J. 68 46
14. Caputo M 1967 Geophys. J. R. Astron. 13 529
15. Carpinteri A and Mainardi F 1997 Fractals and Fractional Calculus in Continuum Mechanics (Wien: Springer)
16. Gorenflo R and Mainardi F 1997 Fractional calculus: integral and differential equations of fractional order Fractals and Fractional Calculus in Continuum Mechanics ed A Carpinteri and F Mainardi (Vienna: Springer) p 223
17. Tenreiro Machado J A 2003 Fraction. Calc. Appl. Anal. 8 73
18. Mainardi F, Luchko Yu and Pagnini G 2001 Fraction. Calc. Appl. Anal. 4 153
19. Liang J, Zhang W, Chen Y Q and Podlubny I 2006 Discrete time fractional order controllers Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering ed J Sabatier, J Machado and O Agrawal (Berlin: Springer)
20. Diethelm K and Ford N J 2002 J. Math. Anal. Appl. 265 229
21. Lorenzo C F and Hartley T T 2004 Nonlinear Dyn. 38 23
22. Luchko Y and Gorenflo R 1999 Acta Math. Vietn. 24 207
23. Momani S and Odibat Z 2008 J. Comput. Appl. Math. 220 010111
24. Frederico G S F and Torres D F M 2007 J. Math. Anal. Appl. 334 834
25. Trujillo J J 1999 J. Math. Anal. Appl. 231 255
26. Atanackovic T M and Stankovic B 2007 Z. Angew. Math. Mech. 87 537
27. Maaraba T A, Jarad F and Baleanu D 2008 Sci. Chin. Ser. A: Math. 51 1775
28. Magin R L, Abdullah O, Baleanu D and Xiaohong J Z 2008 J. Mag. Res. 190 255
29. Heymans N and Podlubny I 2006 Rheol. Acta 45 765
30. Riewe F 1996 Phys. Rev. E 53 1890
31. Klimek M 2001 Czech. J. Phys. 51 1348
32. Agrawal O P 2002 J. Math. Anal. Appl. 272 368
33. Baleanu D and Avkar T 2004 Nuovo Cimento B 119 73
34. Baleanu D 2004 Constrained systems and Riemann-Liouville fractional derivative Proc. 1st IFAC Workshop on Fractional Differentiation and its Applications (Bordeaux, France, July 19-21) p 597
35. Baleanu D 2004 About fractional calculus of singular Lagrangians Proc. IEEE Int. Conf. on Computational Cybernetics ICCC 2004 (Wien, Austria, August 30-September 1) p 379
36. Muslih S I and Baleanu D 2005 J. Math. Anal. Appl. 304 599
37. Baleanu D and Muslih S 2005 Phys. Scr. 72 119
38. Agrawal O P 2006 J. Phys. A: Math. Gen. 39 10375
39. Tarasov V E 2006 J. Phys. A: Math. Gen. 39 8409
40. Agrawal O P 2007 J. Phys. A: Math. Theor. 40 6287
41. Atanackovic T M, Konjik S and Philipovic S 2008 Z. Angew. Math. Mech. 41 095201
42. Cresson J 2007 J. Math. Phys. 48 033504
43. El-Nabulsi R A and Torres D F M 2007 Math. Methods Appl. Sci. 30 1931
44. Baleanu D and Trujillo J J 2008 Nonlinear Dyn. 52 199
45. Riewe F 1997 Phys. Rev. E 55 3581
46. Klimek M 2002 Czech. J. Phys. 52 1247
47. Baleanu D, Muslih S I and Taş K 2006 J. Math. Phys. 47 103503
48. Baleanu D and Agrawal O P 2006 Czech. J. Phys. 56 1087
49. Baleanu D, Muslih S I and Rabei E M 2008 Nonlinear Dyn. 53 67
50. Baleanu D 2008 Rep. Math. Phys. 61 331
51. Baleanu D 2006 Signal Process. 86 2632
52. Baleanu D and Muslih S I 2008 J. Vib. Control. 14 1301
53. Tarasov V E and Zaslavsky G M 2008 J. Math. Phys. 13 1860
54. Rabei E M, Nawafleh K I, Hijjawi R S, Muslih S I and Baleanu D 2007 J. Math. Anal. Appl. 327 891
55. Rabei E M, Almayteh I, Muslih S I and Baleanu D 2008 Phys. Scr. 77 015101
56. Baleanu D, Maraaba T and Jarad F 2008 J. Phys. A: Math. Theor. 41 315403
57. Baleanu D, Golmankhaneh K A and Ali Golmankhaneh K 2008 Int. J. Theor. Phys. 48 1044
58. Bering K A 2000 Note on non-locality and Ostrogradski's construction. arXiv:hep-th/0007192
59. Llosa J 1994 J. Math. Phys. 35 2856