Dynamics with low-level fractionality

Physica A: Statistical Mechanics and its Applications

Volumn 368, Issue 2, 2006, Pages 399-415

  Tarasov, Vasily E ^a,b   Zaslavsky, George M ^a,c  

^a NEW YORK UNIVERSITY   (United States)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

^c POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Fractional equations; Fractional oscillator; Ginzburg Landau equation

Indexed keywords

COMPUTATIONAL COMPLEXITY; FRACTALS; NONLINEAR SYSTEMS; OSCILLATORS (MECHANICAL); STATISTICAL MECHANICS;

FRACTIONAL EQUATIONS; FRACTIONAL OSCILLATORS; GINZBURG-LANDAU EQUATION;

EQUATIONS OF MOTION;

EID: 33744831468     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2005.12.015     Document Type: Article

References (60)

1. R. Hilfer (Ed.), Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
2. Caputo M. Elasticita e Dissipazione (1969), Zanichelli, Bologna
3. Zaslavsky G.M. Phys. Rep. 371 (2002) 461-580
4. Laskin N. Phys. Rev. E 66 (2002) 056108
5. Laskin N. Chaos 10 (2000) 780-790
6. Laskin N. Phys. Rev. E 62 (2000) 3135-3145
7. Laskin N. Phys. Lett. A 268 (2000) 298-305
8. Naber M. J. Math. Phys. 45 (2004) 3339-3352
9. Krisch J.P. J. Math. Phys. 46 (2005) 042506
10. Goldfain E. Chaos Solitons Fractals 22 (2004) 513-520
11. Goldfain E. Chaos Solitons Fractals 19 (2004) 1023-1030
12. Zaslavsky G.M., and Edelman M.A. Physica D 193 (2004) 128-147
13. Saichev A.I., and Zaslavsky G.M. Chaos 7 (1997) 753-764
14. Zaslavsky G.M. Physica D 76 (1994) 110-122
15. Carreras B.A., Lynch V.E., and Zaslavsky G.M. Phys. Plasmas 8 (2001) 5096-5103
16. Nigmatullin R.R. Phys. Status Solidi B 133 (1986) 425-430
17. Nigmatullin R.R. Theor. Math. Phys. 90 (1992) 242-251
18. Le Mehaute A., Nigmatullin R.R., and Nivanen L. Fleches du temps et geometric fractale (1998), Hermes, Paris
19. Tarasov V.E. Phys. Plasmas 12 (2005) 082106
20. Tarasov V.E. Ann. Phys. 318 (2005) 286-307
21. Tarasov V.E. Phys. Lett. A 336 (2005) 167-174
22. Tarasov V.E. Chaos 15 (2005) 023102
23. Zosimov V.V., and Lyamshev L.M. Uspekni Fizicheskih Nauk 165 (1995) 361-402
24. Metzler R., and Klafter J. Phys. Rep. 339 (2000) 1-77
25. E.W. Montroll, M.S. Shlesinger, in: J. Lebowitz, E.W. Montroll (Eds.), Studies in Statistical Mechanics, vol. 11, North-Holland, Amsterdam, 1984, pp. 1-121.
26. Uchaikin V.V., and Zolotarev V.M. Chance and Stability (1999), VSP, Utrecht
27. West B.J., Bologna M., and Grigolini P. Physics of Fractal Operators (2003), Springer, New York
28. Gorenflo R., and Mainardi F. Fractional calculus: integral and differential equations of fractional order. In: Carpinteri A., and Mainardi F. (Eds). Fractals and Fractional Calculus in Continuum Mechanics (1997), Springer, Wien and New York 223-276
29. Gorenflo R., and Mainardi F. J. Comput. Appl. Math. 118 (2000) 283-299
30. Mainardi F. Chaos Solitons Fractals 7 (1996) 1461-1477
31. G.M. Zaslavsky, A.A. Stanislavsky, M. Edelman, Chaotic and pseudochaotic attractors of perturbed fractional oscillator, Chaos, to be published, Preprint: nlin.CD/0508018.
32. Miller K.S., and Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), Wiley, New York
33. Podlubny I. Fractional Differential Equations (1999), Academic Press, New York
34. Weitzner H., and Zaslavsky G.M. Commun. Nonlin. Sci. Numer. Simul. 8 (2003) 273-281
35. Tarasov V.E., and Zaslavsky G.M. Physica A 354 (2005) 249-261
36. Milovanov A.V., and Rasmussen J.J. Phys. Lett. A 337 (2005) 75-80
37. Samko S.G., Kilbas A.A., and Marichev O.I. Fractional Integrals and Derivatives Theory and Applications (1993), Gordon and Breach, New York
38. Oldham K.B., and Spanier J. The Fractional Calculus (1974), Academic Press, New York
39. Gelfand I.M., and Shilov G.E. Generalized Functions I: Properties and Operations (1964), Academic Press, New York
40. Caputo M. Geophys. J. R. Astron. Soc. 13 (1967) 529-539
41. Caputo M., and Mainardi F. Riv. Nuovo Cimento (Ser. II) 1 (1971) 161-198
42. Stanislavsky A.A. Phys. Rev. E 70 (2004) 051103
43. Stanislavsky A.A. Physica A 354 (2005) 101-110
44. Achar B.N.N., Hanneken J.W., and Clarke T. Physica A 339 (2004) 311-319
45. Achar B.N.N., Hanneken J.W., and Clarke T. Physica A 309 (2002) 275-288
46. Achar B.N.N., Hanneken J.W., Enck T., and Clarke T. Physica A 297 (2001) 361-367
47. Tofighi A. Physica A 329 (2003) 29-34
48. Ryabov Y.E., and Puzenko A. Phys. Rev. B 66 (2002) 184201
49. Dzherbashyan M.M. Integral Transform Representations of Functions in the Complex Domain (1966), Nauka, Moscow
50. A. Erdelyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions, vol. 1, Krieger, New York, 1981. pp. 206-227 (Chapter 18).
51. H. Bateman, A. Erdelyi, Tables of Integral Transform, vol. 1, McGraw-Hill, New York, 1954.
52. M. Abramowitz, I.A. Stegun, (Eds.), Sine and cosine integrals, in: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing, Dover, New York, 1972, pp. 231-233 (Section 5.2).
53. Gorenflo R., Loutchko J., and Luchko Y. Fractional Calcul. Appl. Anal. 5 (2002) 491-518
54. Leontovich M.A. Izvestya Akademii Nauk SSSR, Ser. Fiz. 8 (1944) 16
55. Lighthill J. Waves in Fluid (1978), Cambridge University Press, Cambridge (Section 3.7)
56. Kadomtsev B.B. Collective Phenomena in Plasmas (1978), Pergamon, New York (Sections 2.5.5 and 3.4.4)
57. Sagdeev R.Z., Usikov D.A., and Zaslavsky G.M. Nonlinear Physics. From the Pendulum to Turbulence and Chaos (1988), Harwood Academic, New York (Section 15.1)
58. Zaslavsky G.M., and Abdullaev S.S. Chaos 7 (1997) 182-186
59. Woyczynski W.A. In: Berndorff-Nielsen O.E., et al. (Ed). Lévy Processes Theory and Applications (2001), Birkhäuser, Boston 241-266
60. Biler P., Funaki T., and Woyczynski W.A. J. Differential Equations 148 (1998) 9-46