A NOTE ON FRACTAL DIMENSION OF RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL

被引：1

作者：

Chandra, Subhash ^{[1
]}

Abbas, Syed ^{[1
]}

Liang, Yongshun ^{[2
]}

机构：

[1] Indian Inst Technol Mandi, Sch Math & Stat Sci, Kamand 175005, Himachal Prades, India

[2] Nanjing Univ Sci & Technol, Inst Sci, Nanjing 210094, Peoples R China

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2024年 / 32卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Riemann-Liouville Fractional Integral; Bounded Variation; Box Dimension; Hausdorff Dimension; BOUNDED VARIATION;

D O I：

10.1142/S0218348X24400012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper intends to study the analytical properties of the Riemann-Liouville fractional integral and fractal dimensions of its graph on Double-struck capital R-n. We show that the Riemann-Liouville fractional integral preserves some analytical properties such as boundedness, continuity and bounded variation in the Arzela sense. We also deduce the upper bound of the box dimension and the Hausdorff dimension of the graph of the Riemann-Liouville fractional integral of Holder continuous functions. Furthermore, we prove that the box dimension and the Hausdorff dimension of the graph of the Riemann-Liouville fractional integral of a function, which is continuous and of bounded variation in Arzela sense, are n.

引用

页数：14

共 25 条

[1] Properties of functions f(x, y) of bounded variation [J].

Adams, C. Raymond ;

Clarkson, James A. .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1934, 36 (1-4) :711-730

[2]

Adams CR, 1939, T AM MATH SOC, V46, P468

[3]

Agrawal V, 2021, EUR PHYS J-SPEC TOP, V230, P3781, DOI 10.1140/epjs/s11734-021-00304-9

[4]

Barnsley M. F., 1988, Fractals Everywhere

[5] FRACTAL FUNCTIONS AND INTERPOLATION [J].

BARNSLEY, MF .

CONSTRUCTIVE APPROXIMATION, 1986, 2 (04) :303-329

[6] Fractal dimensions of mixed Katugampola fractional integral associated with vector valued functions [J].

Chandra, Subhash ;

Abbas, Syed .

CHAOS SOLITONS & FRACTALS, 2022, 164

[7] Analysis of fractal dimension of mixed Riemann-Liouville integral [J].

Chandra, Subhash ;

Abbas, Syed .

NUMERICAL ALGORITHMS, 2022, 91 (03) :1021-1046

[8] ANALYSIS OF MIXED WEYL-MARCHAUD FRACTIONAL DERIVATIVE AND BOX DIMENSIONS [J].

Chandra, Subhash ;

Abbas, Syed .

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2021, 29 (06)

[9] On definitions of bounded variation for functions of two variables [J].

Clarkson, James A. ;

Adams, C. Raymond .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1933, 35 (1-4) :824-854

[10]

Falconer K., 1990, Fractal Geometry: Mathematical Foundations and Applications, P120

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