Upper Bound Estimation of Fractal Dimensions of Fractional Integral of Continuous Functions

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.

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.

Liang, Y. (2015) Upper Bound Estimation of Fractal Dimensions of Fractional Integral of Continuous Functions.

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.

[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.