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Volume 32, Issue 2
Box Dimension of Weyl Fractional Integral of Continuous Functions with Bounded Variation

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

Anal. Theory Appl., 32 (2016), pp. 174-180.

Published online: 2016-04

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  • Abstract

We know that the Box dimension of $f(x)\in C^1[0,1]$ is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integral of above function is also 1.

  • Keywords

Fractional calculus, box dimension, bounded variation.

  • AMS Subject Headings

28A80, 26A33, 26A30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-32-174, author = {}, title = {Box Dimension of Weyl Fractional Integral of Continuous Functions with Bounded Variation}, journal = {Analysis in Theory and Applications}, year = {2016}, volume = {32}, number = {2}, pages = {174--180}, abstract = {

We know that the Box dimension of $f(x)\in C^1[0,1]$ is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integral of above function is also 1.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2016.v32.n2.6}, url = {http://global-sci.org/intro/article_detail/ata/4663.html} }
TY - JOUR T1 - Box Dimension of Weyl Fractional Integral of Continuous Functions with Bounded Variation JO - Analysis in Theory and Applications VL - 2 SP - 174 EP - 180 PY - 2016 DA - 2016/04 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n2.6 UR - https://global-sci.org/intro/article_detail/ata/4663.html KW - Fractional calculus, box dimension, bounded variation. AB -

We know that the Box dimension of $f(x)\in C^1[0,1]$ is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integral of above function is also 1.

L. Mu, K. Yao, Y. S. Liang & J. Wang. (1970). Box Dimension of Weyl Fractional Integral of Continuous Functions with Bounded Variation. Analysis in Theory and Applications. 32 (2). 174-180. doi:10.4208/ata.2016.v32.n2.6
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