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Volume 32, Issue 3
On the Connection Between the Order of Riemann-Liouville Fractional Calculus and Hausdorff Dimension of a Fractal Function

J. Wang, K. Yao & Y. S. Liang

DOI: 10.4208/ata.2016.v32.n3.6

Anal. Theory Appl., 32 (2016), pp. 283-290.

Published online: 2016-07

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  • Abstract

This paper investigates the fractal dimension of the fractional integrals of a fractal function. It has been proved that there exists some linear connection between the order of Riemann-Liouville fractional integrals and the Hausdorff dimension of a fractal function.

  • Keywords

Fractional calculus, Hausdorff dimension, Riemann-Liouville fractional integral.

  • AMS Subject Headings

MR28A80, MR26A33, MR26A30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-32-283, author = {J. Wang, K. Yao and Y. S. Liang}, title = {On the Connection Between the Order of Riemann-Liouville Fractional Calculus and Hausdorff Dimension of a Fractal Function}, journal = {Analysis in Theory and Applications}, year = {2016}, volume = {32}, number = {3}, pages = {283--290}, abstract = {

This paper investigates the fractal dimension of the fractional integrals of a fractal function. It has been proved that there exists some linear connection between the order of Riemann-Liouville fractional integrals and the Hausdorff dimension of a fractal function.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2016.v32.n3.6}, url = {http://global-sci.org/intro/article_detail/ata/4671.html} }
TY - JOUR T1 - On the Connection Between the Order of Riemann-Liouville Fractional Calculus and Hausdorff Dimension of a Fractal Function AU - J. Wang, K. Yao & Y. S. Liang JO - Analysis in Theory and Applications VL - 3 SP - 283 EP - 290 PY - 2016 DA - 2016/07 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n3.6 UR - https://global-sci.org/intro/article_detail/ata/4671.html KW - Fractional calculus, Hausdorff dimension, Riemann-Liouville fractional integral. AB -

This paper investigates the fractal dimension of the fractional integrals of a fractal function. It has been proved that there exists some linear connection between the order of Riemann-Liouville fractional integrals and the Hausdorff dimension of a fractal function.

J. Wang, K. Yao and Y. S. Liang. (2016). On the Connection Between the Order of Riemann-Liouville Fractional Calculus and Hausdorff Dimension of a Fractal Function. Analysis in Theory and Applications. 32 (3). 283-290. doi:10.4208/ata.2016.v32.n3.6
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