Connection between the order of fractional calculus and fractional dimensions of a type of fractal functions

Analysis in Theory and Applications

Volumn 23, Issue 4, 2007, Pages 354-362

  Liang, Yongshun ^a   Su, Weiyi ^b  

^a NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b NANJING UNIVERSITY   (China)

Author keywords

Fractal dimension; Generalized Weierstrass function; Graph; Linear; Riemann Liouville fractional calculus

Indexed keywords

EID: 38349050508     PISSN: 16724070     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10496-007-0354-8     Document Type: Article

References (13)

1. Falconer, J., Fractal Geometry: Mathematical Foundations and Applications, New York: John Wiley Sons Inc.; 1990.
2. Hu, T. Y. and Lau, K.S., Fractal Dimensions and Singularities of the Weierstrass Type Functions, Trans. Amer. Math. Soc., 335:2(1993), 649-665.
3. Mandelbrot, B. B., The Fractal Geometry of Naturem, Freeman, New York, 1977.
4. Kolwankar, K. M. and Gangal, A. D., Fractional Differentiability of Nowhere Differentiable Functions and Dimensions, Chaos 6:4(1996), 505-513.
5. Ross, B., Fractional Calculus and its Applications, Springer-Verlag Berlin Heidelberg, 1975.
6. Tatom, F. B., The Relationship Between Fractional Calculus and Fractals, Fractals 3:1(1995), 217-229.
7. Wen, Z. Y., Mathematical Foundations of Fractal Geometry, Shanghai: Shanghai Science and Technology Educational Publishing House; 2000[in Chinese].
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. and Ziezold, H., Fractional Derivatives of Weierstrass-type Functions, J Computat Appl. Math., 76(1996), 265-275.
10. Yao, K., Su, W. Y. and Zhou, S. P., On the Fractional Calculus of a Type of Weierstrass Function, Chinese Annals of Mathematics 25:A(2004), 711-716.
11. Liang, Y.S. and Su, W. Y., The Relationship Between the Fractal Dimensions of a Type of Fractal Functions and the Order of Their Fractional Calculus, Chaos, Solitons and Fractals, 34(2007), 682-692.
12. Liang, Y.S. and Yao, K., The Fractal Dimensions of Graphs of the Weyl-Marchaud Fractional Derivative of the Weierstrass Function, International Journal of Nonlinear Sciences and Numerical Simulation (Accept).
13. Yao, K. and Liang, Y. S., The Fractal Dimensions of the Weyl-Marchaud Fractional Derviative of the Weierstrass-type Function, Chaos, Solitons and Fractals(Accept).