The relationship between the fractal dimensions of a type of fractal functions and the order of their fractional calculus

Chaos, Solitons and Fractals

Volumn 34, Issue 3, 2007, Pages 682-692

  Liang, Y S ^a   Su, W Y ^a  

^a NANJING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; DIFFERENTIATION (CALCULUS); FUNCTIONS;

FRACTAL FUNCTIONS; FRACTIONAL CALCULUS; HAUSDORFF DIMENSION;

FRACTAL DIMENSION;

EID: 34247152508     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.01.124     Document Type: Article

References (19)

1. Falconer J. Fractal geometry: mathematical foundations and applications (1990), John Wiley Sons Inc., New York
2. Frostman O. Potentiel d'èquilibre et capacitè des ensembles avec quelques applications s̀ la théorie des fonctions. Meddel Lunds Univ Mat Sem 3 (1935) 1-118
3. Kolwankar K.M., and Gangal A.D. Fractional differentiability of nowhere differentiable functions and dimensions. Chaos 6 4 (1996) 505-513
4. Kolwankar KM. Studies of fractal structures and processes using methods of the fractional calculus. PhD thesis, University of Pune, 1997.
5. Miller K.S., and Ross B. An introduction to the fractional calculus and fractional differential equations (1993), John Wiley Sons Inc., New York
6. Ross B. Fractional calculus and its applications (1975), Springer-Verlag, Berlin, Heidelberg
7. Sun D.C., and Wen Z.Y. The Hausdorff dimension of graphs of a class of Weierstrass functions. Progr Nat Sci 6 3 (1996) 290-295
8. Yao K., Su W.Y., and Zhou S.P. On the connection between the order of fractional calculus and the dimensions of a fractal function. Chaos, Solitons & Fractals 23 (2005) 621-629
9. Zähle M. Fractional differentiation in the self-affine case V - The local degree of differentiability. Math Nachr 185 (1997) 279-306
10. Zähle M., and Ziezold H. Fractional derivatives of Weierstrass-type functions. J Comput Appl Math 76 (1996) 265-275
11. Zhou S.P., He G.L., and Xie T.F. On a class of fractals: the constructive structure. Chaos, Solitons & Fractals 19 (2004) 1099-1104
12. El Naschie M.S. Elementary prerequisites for E-infinity (recommended background readings in nonlinear dynamics, geometry and topology). Chaos, Solitons & Fractals 30 3 (2006) 579-605
13. El Naschie M.S. Intermediate prerequisites for E-infinity theory. Chaos, Solitons & Fractals 30 3 (2006) 622-628
14. El Naschie M.S. Advanced prerequisite for E-infinity theory. Chaos, Solitons & Fractals 30 3 (2006) 636-641
15. El Naschie M.S. On a fuzzy Kähler-like manifold which is consistent with the two slit experiment. Int J Nonlinear Sci Numer Simul 6 2 (2005) 95-98
16. Inovane G., and Varying G. Accelerating universe, and other relevant consequences of a stochastic self-similar and fractal universe. Chaos, Solitons & Fractals 20 (2004) 657-667
17. ∞ manifold and high energy particle physics. Chaos, Solitons & Fractals 20 (2004) 669-682
18. El Naschie M.S. How gravitational instanton could solve the standard model of high energy practical physics. Chaos, Solitons & Fractals 21 (2004) 249-260
19. El Naschie M.S. Quantum gravity from descriptive set theory. Chaos, Solitons & Fractals 19 (2004) 1339-1344