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

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

Published online: 2016-04

Cited by

Export citation
• 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.

28A80, 26A33, 26A30

• BibTex
• RIS
• TXT
@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
Copy to clipboard
The citation has been copied to your clipboard