Weyl quantization of fractional derivatives

Journal of Mathematical Physics

Volumn 49, Issue 10, 2008, Pages

  Tarasov, Vasily E ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 55349146267     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3009533     Document Type: Article

References (20)

1. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Application of Fractional Differential Equations (Elsevier, Amsterdam, 2006).
2. K. B. Oldham and J. Spanier, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order (Academic, New York, 1974).
3. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives Theory and Applications (Gordon and Breach, New York, 1993).
4. K. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley, New York, 1993).
5. I. Podlubny, Fractional Differential Equations (Academic, San Diego, 1999).
6. G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics (Oxford University Press, Oxford, 2005).
7. Fractals and Fractional Calculus in Continuum Mechanics, edited by, A. Carpinteri, and, F. Mainardi, (Springer, Wien, 1997).
8. Applications of Fractional Calculus in Physics, edited by, R. Hilfer, (World Scientific, Singapore, 2000).
9. G. M. Zaslavsky, Phys. Rep. 0370-1573 10.1016/S0370-1573(02)00331-9 371, 461 (2002).
10. E. W. Montroll and M. F. Shlesinger, in Studies in Statistical Mechanics, edited by, J. Lebowitz, and, E. Montroll, (North-Holland, Amsterdam, 1984), Vol. 11, pp. 1-121.
11. Advances in Fractional Calculus. Theoretical Developments and Applications in Physics and Engineering, edited by, J. Sabatier, O. P. Agrawal, and, J. A. Tenreiro Machado, (Springer, Berlin, 2007).
12. V. E. Tarasov, Phys. Lett. A 0375-9601 10.1016/S0375-9601(01)00548-5 288, 173 (2001).
13. V. E. Tarasov, Quantum Mechanics of Non-Hamiltonian and Dissipative Systems (Elsevier, Amsterdam, 2008).
14. K. Yosida, Functional Analysis (Springer, Berlin, 1965).
15. F. A. Berezin and M. A. Shubin, The Schrodinger Equation (Kluwer Academic, Dordrecht, 1991).
16. N. L. Balazs and B. K. Jennings, Phys. Rep. 0370-1573 10.1016/0370-1573(84)90151-0 104, 347 (1984).
17. V. E. Tarasov, Phys. Lett. A 0375-9601 10.1016/j.physleta.2008.01.037 372, 2984 (2008).
18. V. E. Tarasov, J. Math. Phys. 0022-2488 10.1063/1.2337852 47, 092901 (2006).
19. R. Metzler and J. Klafter, Phys. Rep. 0370-1573 10.1016/S0370-1573(00) 00070-3 339, 1 (2000).
20. G. Lindblad, Rep. Math. Phys. 0034-4877 10.1016/0034-4877(76)90029-X 10, 393 (1976).