Fractal dimension of Riemann-Liouville fractional integral of 1-dimensional continuous functions

被引：0

作者：

Yong Shun Liang

机构：

[1] Nanjing University of Science and Technology,Institute of Science

来源：

Fractional Calculus and Applied Analysis | 2018年 / 21卷

关键词：

Primary 26A30; Secondary 28A33; Box dimension; Riemann-Liouville fractional integral; variation;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The present paper investigates fractal dimension of fractional integral of continuous functions whose fractal dimension is 1 on [0, 1]. For any continuous functions whose Box dimension is 1 on [0, 1], Riemann-Liouville fractional integral of these functions of any positive order has been proved to still be 1-dimensional continuous functions on [0, 1].

引用

页码：1651 / 1658

页数：7

共 50 条

[1] FRACTAL DIMENSION OF RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL OF 1-DIMENSIONAL CONTINUOUS FUNCTIONS
Liang, Yong Shun
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2018, 21 (06) : 1651 - 1658
[2] UPPER BOX DIMENSION OF RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL OF FRACTAL FUNCTIONS
Liang, Y. S.
Wang, H. X.
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2021, 29 (01)
[3] A NOTE ON FRACTAL DIMENSION OF RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL
Chandra, Subhash
Abbas, Syed
Liang, Yongshun
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2024, 32 (02)
[4] THE EFFECTS OF THE RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL ON THE BOX DIMENSION OF FRACTAL GRAPHS OF HOLDER CONTINUOUS FUNCTIONS
Wu, Junru
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2020, 28 (03)
[5] RELATIONSHIP OF UPPER BOX DIMENSION BETWEEN CONTINUOUS FRACTAL FUNCTIONS AND THEIR RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL
Xiao, Wei
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2021, 29 (08)
[6] FRACTAL DIMENSION OF RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL OF CERTAIN UNBOUNDED VARIATIONAL CONTINUOUS FUNCTION
Li, Yang
Xiao, Wei
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2017, 25 (05)
[7] COMPOSITION OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS AND THEIR RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL
Yu, Bin
Zhang, Tao
Yao, Lei
Zhao, Wei
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2019, 27 (04)
[8] The Relationship between the Box Dimension of Continuous Functions and Their (k,s)-Riemann-Liouville Fractional Integral
Wang, Bingqian
Xiao, Wei
Choi, Junesang
[J]. SYMMETRY-BASEL, 2023, 15 (12):
[9] Analysis of fractal dimension of mixed Riemann-Liouville integral
Chandra, Subhash
Abbas, Syed
[J]. NUMERICAL ALGORITHMS, 2022, 91 (03) : 1021 - 1046
[10] Analysis of fractal dimension of mixed Riemann-Liouville integral
Subhash Chandra
Syed Abbas
[J]. Numerical Algorithms, 2022, 91 : 1021 - 1046

← 1 2 3 4 5 →