CONSTRUCTION OF SOME SPECIAL CONTINUOUS FUNCTIONS AND ANALYSIS OF THEIR FRACTIONAL INTEGRALS

Jinmyong Kim and Myongjin Kim
Additional contact information
Jinmyong Kim: Faculty of Mathematics, Kim Il Sung University, Pyongyang, DPR Korea
Myongjin Kim: Pyongyang Soft Joint Development Centre, Pyongyang, DPR Korea

FRACTALS (fractals), 2021, vol. 29, issue 07, 1-9

Abstract: In this paper, we mainly construct two continuous functions defined on I = [0, 1] which have only one unbounded variation point, and show that both Box and Hausdorff dimensions of these functions are 1. We prove that their Riemann–Liouville fractional integrals are bounded variation function. We also show that these functions repair inaccuracies of the example in [N. Liu and K. Yao, Fractal dimension of a special continuous function, Fractals 26(4) (2018) 1850048; Y. S. Liang, Definition and classification of one-dimensional continuous functions with unbounded variation, Fractals 25(5) (2017) 1750048]. In the proofs, we mainly use Leibniz’s alternating series test and the properties of logarithmic function.

Keywords: Unbounded Variation; Hausdorff Dimension; Box Dimension; Fractional Integral; Continuous Function (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X21502340
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:29:y:2021:i:07:n:s0218348x21502340

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X21502340

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().