A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems

European Physical Journal: Special Topics

Volumn 193, Issue 1, 2011, Pages 185-192

  Sun, H G ^a   Chen, W ^a   Wei, H ^a   Chen, Y Q ^b  

^a HOHAI UNIVERSITY   (China)

^b Utah State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79953691444     PISSN: 19516355     EISSN: 19516401     Source Type: Journal    
DOI: 10.1140/epjst/e2011-01390-6     Document Type: Article

References (41)

1. S. Westerlund, Phys. Scripta 43, 174 (1991).
2. C. F. M. Coimbra, Ann. Phys. (Leipzig) 12, 692 (2003).
3. D. Ingman, J. Suzdalnitsky, M. Zeifman, J. Appl. Mech. 67, 383 (2000).
4. D. Ingman, J. Suzdalnitsky, J. Eng. Mech. 131, 763 (2005).
5. R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000).
6. F. Mainardi, A. Mura, G. Pagnini, R. Gorenflo, J. Vib. Contr. 14, 1267 (2008).
7. H. G. Sun, W. Chen, Y. Q. Chen, Phys. A 388, 4586 (2009).
8. A. W. Lo, Econometrica 59, 1279 (1991).
9. S. Z. Rida, A. M. A. El-Sayed, A. A. M. Arafa, J. Stat. Phys. 140, 797 (2010).
10. B. J. West, E. L. Geneston, P. Grigolini, Phys. Rep. 468, 1 (2008).
11. C. P. Li, W. G. Sun, New Trends Nanotechnol. Fract. Calcul. Appl. 3, 243 (2010).
12. A. J. Turski, B. Atamaniuk, E. Turska, J. Tech. Phys. 44, 193 (2003).
13. R. L. Bagley, Torvik P. J., Int. J. Appl. Math. 2, 865 (2000).
14. I. M. Sokolov, A. V. Chechkin, J. Klafter, Acta Phys. Pol. B 35, 1323 (2004).
15. C. P. Li, W. H. Deng, Appl. Math. Comput. 187, 777 (2007).
16. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
17. C. A. Monje, Y. Q. Chen, B. M. Vinagre, D. Y. Xue, V. Feliu, Fractional-order Systems and Controls (Springer-Verlag, London, 2010).
18. F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticy (Imperial College Press, London, 2010).
19. E. N. de Azevedo, P. L. de Sousa, R. E. de Souza, M. Engelsberg, M. de N. do N. Miranda, M. A. Silva, Phys. Rev. E 73, 011204 (2006).
20. Y. He, S. Burov, R. Metzler, E. Barkai, Phys. Rev. Lett. 101, 058101 (2008).
21. K. Weron, M. Kotulski, Phys. A 232, 180 (1996).
22. S. G. Samko, B. Ross, Integral Trans. Spec. Funct. 1, 277 (1993).
23. S. G. Samko, J. Anal. Math. 21, 213 (1995).
24. A. V. Chechkin, R. Gorenflo, I. M. Sokolov, J. Phys. A: Math. Gen. 38, L679 (2005).
25. A. V. Chechkin, V. Yu. Gonchar, R. Gorenflo, N. Korabel, I. M. Sokolov, Phys. Rev. E 78, 021111 (2008).
26. Ya. L. Kobelev, L. Ya. Kobelev, Yu. L. Klimontovich, Dokl. Phys. 48, 285 (2003).
27. C. F. Lorenzo, T. T. Hartley, Nonlinear Dyn. 29, 57 (2002).
28. H. G. Sun, W. Chen, H. Sheng, Y. Q. Chen, Phys. Lett. A 374, 906 (2010).
29. B. Ross, S. K. Samko, Int. J. Math. Math. Sci. 18, 777 (1995).
30. C. M. Soon, C. F. M. Coimbra, M. H. Kobayashi, Ann. Phys. (Leipzig) 14, 378 (2005).
31. R. Metzler, J. Klafter, J. Non-Crystalline Solids 305, 81 (2002).
32. F. Mainardi, Chaos, Soliton & Fractal 7, 1461 (1996).
33. V. V. Anh, J. M. Angulo, M. D. Ruiz-Medina, Nonlinear Ana. 63, e2043 (2005).
34. J. D. Bao, Y. Z. Zhuo, Phys. Rev. Lett. 91, 138104 (2003).
35. N. Heymans, I. Podlubny, Rheol. Acta. 45, 765 (2006).
36. H. G. Sun, Y. Q. Chen, W. Chen, Signal Processing 91, 525 (2011).
37. K. Diethelm, N. J. Ford, A. D. Freed, Nonlinear Dyn. 29, 3 (2002).
38. T. A. M. Langlands, B. I. Henry, J. Comp. Phys. 205, 719 (2005).
39. H. G. Sun, Y. Q. Chen, W. Chen, 2010, http://www. mathworks. com/matlabcentral/fileexchange/26407.
40. P. Zhuang, F. Liu, V. Anh, I. Turner, SIAM J. Numer. Anal. 47, 1760 (2009).
41. P. Zhuang, F. Liu, V. Anh, I. Turner, SIAM J. Numer. Anal. 47, 1760 (2009).