Quantization of classical fields with fractional derivatives

Nuovo Cimento della Societa Italiana di Fisica B

Volumn 120, Issue 5, 2005, Pages 507-512

  Muslih, S I ^a,b   Baleanu, D ^c,d  

^a AL AZHAR UNIVERSITY   (Palestine)

^b ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

^c CANKAYA UNIVERSITY   (Turkey)

^d INSTITUTE OF SPACE SCIENCES   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 28744434468     PISSN: 15949982     EISSN: None     Source Type: Journal    
DOI: 10.1393/ncb/i2005-10055-x     Document Type: Article

References (35)

1. MILLER K. S. and ROSS B., An Introduction to the Fractional Integrals and Derivatives-Theory and Applications (John Wiley and Sons, New York) 1993.
2. SAMKO S. G., KILBAS A. A. and MARICHEV O. I., Fractional Integrals and Derivatives-Theory and Applications (John Wiley and Sons, New York) 1993.
3. OLDHAM K. B. and SPANIER J., The Fractional Calculus (Academic Press, New York) 1974.
4. PODLUBNY I., Fractional Differential Equations (Academic Press, New York) 1999.
5. GORENFLO R. and MAINARDI F., Fractional Calculus: Integral and Differential Equations of Fractional Orders, Fractals and Fractional Calculus in Continuum Mechanics (Springer Verlag, Wien and New York) 1997.
6. HILFER R., Applications of Fraction Calculus in Physics (World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong) 2000.
7. TENREIRO MACHADO J. A., Fract. Calc. Appl. Anal., 8 (2003) 73;
8. TENREIRO MACHADO J. A., Fract. Calc. Appl. Anal., 4 (2001) 47.
9. KLIMEK M., Czech. J. Phys., 51 (2001) 1348;
10. KLIMEK M., Czech. J. Phys., 52 (2002) 1247.
11. AGRAWAL O. P., Trans. ASME J. Vib. Acoust., 126 (2004).
12. AGRAWAL O. P., GREGORY J. and SPECTOR K. P., J. Math. Ann. Appl., 210 (1997) 702.
13. NONNENMACHER T. F., J. Phys. A, 23 (1990) L697S.
14. METZLER R. and JOSEPH K., Physica A, 278 (2000) 107.
15. ZASLAVSKY G. M., Phys. Rep., 371 (2002) 461.
16. RIEWE F., Phys. Rev. E, 53 (1996) 1890.
17. RIEWE F., Phys. Rev. E, 55 (1997) 3581.
18. AGRAWAL O. P., J. Math. Anal. Appl., 272 (2002) 368.
19. AGRAWAL O. P., J. Math. Anal. Appl., 68 (2001) 339.
20. RASPINI A., Fizika B, 9 (2000) 49.
21. RASPINI A., Physica Scripta, 46 (2000) 20.
22. GAIES A. and EL-AKRMI A., Physica Scripta, 70 (2004) 7.
23. DIRAC P. A. M., Lectures on Quantum Mechanics (Yeshiva University, New York) 1964;
24. SUNDERMEYER K., Constrained Dynamics, Lect. Notes Phys., Vol. 169 (Springer, New York) 1982;
25. HENNEAUX M. and TEITELBOIM C., Quantization of Gauge Systems (Princeton Univ. Press) 1992;
26. HANSON A., REGGE T. and TEITELBOIM C., Constrained Hamiltonian Systems (Academia Nazionale dei Lincei, Rome) 1976.
27. BALEANU D. and AVKAR T., Nuovo Cimento B, 119 (2004) 73.
28. st IFAC Workshop on Fractional Differentiation and its Applications, Bordeaux, France, July 19-21 (2004), pp. 597-602.
29. MUSLIH S. and BALEANU D., J. Math. Anal. Appl., 304 (2005) 599.
30. LLOSA J. and VIVES J., J. Math. Phys., 35 (1994) 2856.
31. SEIBERG N., SUSSKIND L. and TOUMBAS T., JHEP, 0006 (2000) 044.
32. GOMIS J., KAMIMURA K. and LLOSA J., Phys. Rev. D, 63 (2001) 045003.
33. GOMIS J., KAMIMURA K. and RAMIREZ T., Nucl. Phys. B, 696 (2004) 263.
34. BALEANU D. and MUSLIH S., to appear in Physica Scripta.
35. LOVE E. R. and YOUNG L. C., London Math. Soc., 44 (1938) 1.