APM  Vol.5 No.1 , January 2015
Upper Bound Estimation of Fractal Dimensions of Fractional Integral of Continuous Functions
Author(s) Yongshun Liang*
ABSTRACT
Fractional integral of continuous functions has been discussed in the present paper. If the order of Riemann-Liouville fractional integral is v, fractal dimension of Riemann-Liouville fractional integral of any continuous functions on a closed interval is no more than 2 - v.

Cite this paper
Liang, Y. (2015) Upper Bound Estimation of Fractal Dimensions of Fractional Integral of Continuous Functions. Advances in Pure Mathematics, 5, 27-30. doi: 10.4236/apm.2015.51003.
References
[1]   Liang, Y.S. (2010) Box Dimension of Riemann-Liouville Fractional Integral of Continuous Function of Bounded Variation. Nonlinear Analysis Series A: Theory, Method and Applications, 72, 2758-2761.

[2]   Yao, K. and Liang, Y.S. (2010) The Upper Bound of Box Dimension of the Weyl-Marchaud Derivative of Self-Affine Curves. Analysis Theory and Application, 26, 222-227. http://dx.doi.org/10.1007/s10496-010-0222-9

[3]   Liang, Y.S. and Su, W.Y. (2011) The Von Koch Curve and Its Fractional Calculus. Acta Mathematic Sinica, Chinese Series [in Chinese], 54, 1-14.

[4]   Zhang, Q. and Liang, Y.S. (2012) The Weyl-Marchaud Fractional Derivative of a Type of Self-Affine Functions. Applied Mathematics and Computation, 218, 8695-8701.
http://dx.doi.org/10.1016/j.amc.2012.01.077

[5]   Falconer, J. (1990) Fractal Geometry: Mathematical Foundations and Applications. John Wiley Sons Inc., New York.

[6]   Oldham, K.B. and Spanier, J. (1974) The Fractional Calculus. Academic Press, New York.

 
 
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