Fractal dimension of Katugampola fractional integral of continuous functions with unbounded variation

Wenliang Peng,Kui Yao,Yongshun Liang

doi:10.1109/ccdc.2019.8832881

Fractal dimension of Katugampola fractional integral of continuous functions with unbounded variation

Wenliang Peng, Kui Yao + Show 1 more

https://doi.org/10.1109/ccdc.2019.8832881

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Publication Date: Jun 1, 2019

Citations: 1

Affiliation: PLA Army Engineering University, Nanjing University of Science and Technology, Shanghai Institute for Science of Science

#Unbounded Variation #Integral Of Functions + Show 8 more

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Abstract

The present paper mainly explore fractal dimension of Katugampola fractional integral of continuous functions with unbounded variation. We prove that Box dimension and Hausdorff dimension of Katugampola fractional integral of continuous functions with finite unbounded variation points are 1. Furthermore, we get an important conclusion that Box dimension and Hausdorff dimension of Katugampola fractional integral of continuous functions with infinite and countable unbounded variation points are 1.

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