Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


Preferences help
enabled [disable] Abstract
Number of results

Journal

2010 | 8 | 1 | 120-125

Article title

Fractional Newtonian mechanics

Content

Title variants

Languages of publication

EN

Abstracts

EN
In the present paper, we have introduced the generalized Newtonian law and fractional Langevin equation. We have derived potentials corresponding to different kinds of forces involving both the right and the left fractional derivatives. Illustrative examples have worked out to explain the formalism.

Contributors

  • Theoretical Physics Department, Kazan State University, Kremlevskaya str., 18 Kazan, 420008, Tatarstan, Russian Federation
  • Department of Physics, Islamic Azad Uinversity-Oromiyeh Branch, Oromiyeh, PO Box 969, Iran

References

  • [1] K. B. Oldham, J. Spanier, The Fractional Calculus (Academic, New York, 1974)
  • [2] K. S. Miller, B. Ross, An Introduction to the Fractional Integrals and Derivatives-Theory and Application (Wiley, New York, 1993)
  • [3] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives Theory and Applications (Gordon and Breach, New York 1993)
  • [4] R. Hilfer, Aplication of Fractional Calculus in Physics (World Sintific, 2000)
  • [5] I. Podlubny, Fractional Differential Equations (Academic, New York, 1999)
  • [6] G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics (Oxford University Press, 2005)
  • [7] A. A. Kilbas, H. H. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, The Netherlands, 2006)
  • [8] R. L. Magin, Fractional Calculus in Bioengineering (Begell House Publisher, Inc. Connecticut, 2006)
  • [9] R. Gorenflo, F. Mainardi, Fractional Calculus: Integral and Differential Equations of Fractional Orders, Fractals and Fractional Calculus in Continuum Mechanics (Springer Verlag, New York, 1997)
  • [10] B. J. West, M. Bologna, P. Grigolini, Physics of Fractal operators (New York, Springer, 2003)
  • [11] K. M. Kolwankar, A. D. Gangal, Chaos 6, 505 (1996) http://dx.doi.org/10.1063/1.166197[Crossref]
  • [12] K. M. Kolwankar, A. D. Gangal, Phys. Rev. Lett. 80, 214 (1998) http://dx.doi.org/10.1103/PhysRevLett.80.214[Crossref]
  • [13] N. Heymans, I. Podlubny, Rheol. Acta 45, 765 (2006) http://dx.doi.org/10.1007/s00397-005-0043-5[Crossref]
  • [14] T. H. Solomon, E. R. Weeks, H. L. Swinney, Phys. Rev. Lett. 71, 3975 (1993) http://dx.doi.org/10.1103/PhysRevLett.71.3975[Crossref]
  • [15] M. A. Fogleman, M. J. Fawcett, T. H. Solomon, Phys. Rev. E 63, 020101 (2001) http://dx.doi.org/10.1103/PhysRevE.63.020101[Crossref]
  • [16] A. Le Mehaute, R. R. Nigmatullin, L. Nivanen, Fleches du Temps et Geometrie Fractale (Paris, Editions Hermes, 1998)
  • [17] R. R. Nigmatullin, A. Le Mehaute, J. Non-Cryst. Solids 351, 2888 (2005) http://dx.doi.org/10.1016/j.jnoncrysol.2005.05.035[Crossref]
  • [18] R. R. Nigmatullin, Physica A 363, 282 (2006) http://dx.doi.org/10.1016/j.physa.2005.08.033[Crossref]
  • [19] R. R. Nigmatullin et al., Physica B 388, 418 (2007) http://dx.doi.org/10.1016/j.physb.2006.06.153[Crossref]
  • [20] F. Riewe, Phys. Rev. E 53, 1890 (1996) http://dx.doi.org/10.1103/PhysRevE.53.1890[Crossref]
  • [21] F. Riewe, Phys. Rev. E 55, 3581 (1997) http://dx.doi.org/10.1103/PhysRevE.55.3581[Crossref]
  • [22] N. Laskin, Phys. Rev. E 62, 3135 (2000) http://dx.doi.org/10.1103/PhysRevE.62.3135[Crossref]
  • [23] M. Klimek, Czech. J. Phys. 51, 1348 (2001) http://dx.doi.org/10.1023/A:1013378221617[Crossref]
  • [24] M. Klimek, Czech. J. Phys. 52, 1247 (2002) http://dx.doi.org/10.1023/A:1021389004982[Crossref]
  • [25] G. M. Zaslavsky, Phys. Rep. 371, 461 (2002) http://dx.doi.org/10.1016/S0370-1573(02)00331-9[Crossref]
  • [26] M. Klimek, Czech. J. Phys. 55, 1447 (2005) http://dx.doi.org/10.1007/s10582-006-0024-7[Crossref]
  • [27] V. E. Tarasov, G. M. Zaslavsky, Physica A 354, 249 (2005) http://dx.doi.org/10.1016/j.physa.2005.02.047[Crossref]
  • [28] S. Muslih, D. Baleanu, J. Math. Anal. Appl. 304, 599 (2005) http://dx.doi.org/10.1016/j.jmaa.2004.09.043[Crossref]
  • [29] D. Baleanu, S. Muslih, Phys. Scripta 72, 119 (2005) http://dx.doi.org/10.1238/Physica.Regular.072a00119[Crossref]
  • [30] S. Muslih, D. Baleanu, J. Math. Anal. Appl. 304, 599 (2005) http://dx.doi.org/10.1016/j.jmaa.2004.09.043[Crossref]
  • [31] D. Baleanu, O. P. Agrawal, Czech. J. Phys. 56, 1087 (2006) http://dx.doi.org/10.1007/s10582-006-0406-x[Crossref]
  • [32] D. Baleanu, S. Muslih, K. Tas, J. Math. Phys. 47, 103503 (2006) http://dx.doi.org/10.1063/1.2356797[Crossref]
  • [33] V. E Tarasov, Chaos 16, 033108 (2006) http://dx.doi.org/10.1063/1.2219701[Crossref]
  • [34] V. E Tarasov, J. Phys. A-Math. Gen. 39, 8409 (2006) http://dx.doi.org/10.1088/0305-4470/39/26/009[Crossref]
  • [35] E. M. Rabei, K. I. Nawafleh, R. S. Hiijawi, S. I. Muslih, D. Baleanu, J. Math. Anal. Appl. 327, 891 (2007) http://dx.doi.org/10.1016/j.jmaa.2006.04.076[Crossref]
  • [36] E. M. Rabei, I. Almayteh, S. I. Muslih, D. Baleanu, Phys. Scripta 77, 015101 (2007) http://dx.doi.org/10.1088/0031-8949/77/01/015101[Crossref]
  • [37] E. M. Rabei, D. M. Tarawneh, S. I. Muslih, D. Baleanu, J. Vib. Control 13, 1239 (2007) http://dx.doi.org/10.1177/1077546307077469[Crossref]
  • [38] S. F. Gastao Frederico, F. M. T. Delfim, J. Math. Anal. Appl. 334, 834 (2007) http://dx.doi.org/10.1016/j.jmaa.2007.01.013[Crossref]
  • [39] D. Baleanu, A. K. Golmankhaneh, A. K. Golmankhaneh, Int. J. Theor. Phys. 48, 1044 (2009) http://dx.doi.org/10.1007/s10773-008-9877-9[Crossref]
  • [40] O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002) http://dx.doi.org/10.1016/S0022-247X(02)00180-4[Crossref]
  • [41] O. P. Agrawal, J. Phys. A-Math. Gen. 39, 10375 (2006) http://dx.doi.org/10.1088/0305-4470/39/33/008[Crossref]
  • [42] O. P. Agrawal, Journal of Physics A: Mathematical and Theoretical 40, 5469 (2007) http://dx.doi.org/10.1088/1751-8113/40/21/001[WoS][Crossref]
  • [43] E. M. Rabei, I. Almayteh, S. Muslih, D. Baleanu, Phys. Scripta 77, 015101 (2008) http://dx.doi.org/10.1088/0031-8949/77/01/015101[Crossref]
  • [44] D. Baleanu, O. P. Agrawal, Czech. J. Phys. E 56, 1087 (2006) http://dx.doi.org/10.1007/s10582-006-0406-x[Crossref]
  • [45] D. Baleanu, Journal of Computational and Nonlinear Dynamics 3, 021102 (2008) http://dx.doi.org/10.1115/1.2833586[WoS][Crossref]
  • [46] D. Baleanu, J. J. Trujillo, Nonlinear Dynam. 52, 331 (2008) http://dx.doi.org/10.1007/s11071-007-9281-7[Crossref]

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-009-0085-x
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.