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2010 | 8 | 1 | 120-125
Tytuł artykułu

Fractional Newtonian mechanics

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Wydawca

Czasopismo
Rocznik
Tom
8
Numer
1
Strony
120-125
Opis fizyczny
Daty
wydano
2010-02-01
online
2009-11-15
Twórcy
  • Theoretical Physics Department, Kazan State University, Kremlevskaya str., 18 Kazan, 420008, Tatarstan, Russian Federation, nigmat@knet.ru
Bibliografia
  • [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]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-009-0085-x
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