Constant curvature coefficients and exact solutions in fractional gravity and geometric mechanics

Central European Journal of Physics

Volumn 9, Issue 5, 2011, Pages 1267-1279

  Baleanu, Dumitru ^a   Vacaru, Sergiu I ^b  

^a CANKAYA UNIVERSITY   (Turkey)

^b ALEXANDRU IOAN CUZA UNIVERSITY OF IASI   (Romania)

Author keywords

fractional geometry; fractional gravity; generalized Finsler geometry; nonholonomic manifold; nonlinear connection

Indexed keywords

EID: 80052764230     PISSN: 18951082     EISSN: 16443608     Source Type: Journal    
DOI: 10.2478/s11534-011-0040-5     Document Type: Article

References (35)

1. S. Anco, J. Phys. A: Math. Gen. 39, 2043 (2006).
2. S. Anco, S. Vacaru, J. Geom. Phys. 59, 79 (2009).
3. C. Athorne, J. Phys. A: Math. Gen. 21, 4549 (1998).
4. D. Baleanu, S. Vacaru, Nonlin. Dyn. 64, 365 (2011).
5. D. Baleanu, S. Vacaru, Int. J. Phys. 50, 233 (2001).
6. D. Baleanu, S. Vacaru, arXiv: 1007. 2866v3 [math-ph].
7. K. S. Chou, C. Qu, J. Phys. Soc. Japan 70, 1912 (2001).
8. R. E. Goldstein, D. M. Petrich, Phys. Rev. Lett. 67, 3203 (1991).
9. S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces (Amer. Math. Soc., Providence, 2001).
10. J. Langer, R. Perline, Phys. Lett. A 239, 36 (1998).
11. G. L. Lamb, Jr., J. Math. Phys. 18, 1654 (1977).
12. G. Mari Beffa, J. Sanders, J. P. Sanders, J. Nonlinear. Sci. 12, 143 (2002).
13. R. Miron and M. Anastasiei, The Geometry of Lagrange Spaces: Theory and Applications, FTPH no. 59, (Kluwer Academic Publishers, Dordrecht, Boston, London, 1994).
14. K. Nakayama, H. Segur, M. Wadati, Phys. Rev. Lett. 69, 2606 (1992).
15. J. Sanders, J. P. Wang, Mosc. Math. J. 3, 1369 (2003).
16. R. W. Sharpe, Differential Geometry, (Springer-Verlag, New York, 1997).
17. V. E. Tarasov, Ann. Phys. (NY) 323, 2756 (2008).
18. S. Vacaru, Int. J. Geom. Meth. Mod. Phys. 5, 473 (2008).
19. S. Vacaru, Acta Appl. Math. 110, 73 (2010).
20. S. Vacaru, arXiv: 1004. 0625v1 [math. DG].
21. S. Vacaru, arXiv: 1004. 0628v1 [math-ph].
22. A. A. Kilbas, H. H. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, (Elsevier, Amsterdam, 2006).
23. S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives - Theory and Applications (Gordon and Breach, Linghorne, P. A., 1993).
24. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego CA, (1999).
25. R. L. Magin, Fractional Calculus in Bioengineering, Begell House Publisher, Inc. Connecticut, (2006).
26. R. Gorenflo, F. Mainardi, Fractional calculus: Integral and Differential Equations of Fractional Orders, Fractals and Fractional Calculus in Continoum Mechanics, Springer Verlag, Wien and New York (1997).
27. R. Metzler, J. Klafter, J. Phys. A: Math. Gen. 37, 1505 (2004).
28. I. M. Sokolov, J. Klafter, A. Blumen, Physics Today 55, 48 (2002).
29. F. Mainardi, Chaos Sol. Frac. 7, 1461 (1996).
30. O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002).
31. M. Klimek, Czech. J. Phys. 52, 1247 (2002).
32. E. M. Rabei, K. I. Nawafleh, R. S. Hijjawi, S. I. Muslih, D. Baleanu, J. Math. Anal. Appl. 327, 891 (2007).
33. D. Baleanu, S. I. Muslih, Phys. Scripta 72, 119 (2005).
34. R. L. Magin, X. Feng, D. Baleanu, Concept. Magn. Reson. A 34A, 16 (2009).
35. M. F. Silva, J. A. Tenreiro Machado, A. M. Lopes, Robotica 23, 595 (2005).