The relationship between the order of (k, s)-Riemann-Liouville fractional integral and the fractal dimensions of a fractal function

被引：3
|
作者：
Navish, A. A. [1 ]
Priya, M. [1 ]
Uthayakumar, R. [1 ]
机构：
[1] Gandhigram Rural Inst, Dept Math, Dindigul 624302, Tamil Nadu, India
来源：
JOURNAL OF ANALYSIS | 2023年 / 31卷 / 01期
关键词：
(k; s)-Riemann-Liouville fractional integral; Fractal dimension; Weierstrass function; Fractional integral; CALCULUS; INEQUALITIES;
D O I：
10.1007/s41478-022-00451-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper mainly investigates the relationship between the fractal dimension of the graph of the (k, s)-Riemann-Liouville fractional integral and the order of the fractional integral of the famous fractal function known as Weierstrass function. This article inspects several fractal dimensions, like box dimension, packing dimension, K-dimension of the graph of the (k, s)-Riemann-Liouville fractional integral and gives the connection between them. Our result is manifested by varying the order of fractional integral. Supporting results are derived and the related fractal dimension can be seen in the graphical representation.
引用
收藏
页码：261 / 277
页数：17
相关论文
共 50 条
  • [21] FRACTAL DIMENSION OF RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL OF 1-DIMENSIONAL CONTINUOUS FUNCTIONS
    Liang, Yong Shun
    FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2018, 21 (06) : 1651 - 1658
  • [22] THE EFFECTS OF THE RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL ON THE BOX DIMENSION OF FRACTAL GRAPHS OF HOLDER CONTINUOUS FUNCTIONS
    Wu, Junru
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2020, 28 (03)
  • [23] Some integral inequalities for (k, s) - Riemann-Liouville fractional operators
    Houas, Mohamed
    Dahmani, Zoubir
    Sarikaya, Mehmet Zeki
    JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2018, 21 (7-8) : 1575 - 1585
  • [24] Dimension of Riemann-Liouville fractional integral of Takagi function
    Liu, Ning
    Yao, Kui
    Liang, Yong Shun
    PROCEEDINGS OF THE 30TH CHINESE CONTROL AND DECISION CONFERENCE (2018 CCDC), 2018, : 2376 - 2380
  • [25] The relationship between the fractal dimensions of a type of fractal functions and the order of their fractional calculus
    Liang, Y. S.
    Su, W. Y.
    CHAOS SOLITONS & FRACTALS, 2007, 34 (03) : 682 - 692
  • [26] Geometric Interpretation for Riemann-Liouville Fractional-Order Integral
    Bai, Lu
    Xue, Dingyu
    Meng, Li
    PROCEEDINGS OF THE 32ND 2020 CHINESE CONTROL AND DECISION CONFERENCE (CCDC 2020), 2020, : 3225 - 3230
  • [27] ON THE SET OF SOLUTIONS OF FRACTIONAL ORDER RIEMANN-LIOUVILLE INTEGRAL INCLUSIONS
    Abbas, Said
    Benchohra, Mouffak
    DEMONSTRATIO MATHEMATICA, 2013, 46 (02) : 271 - 281
  • [28] Riemann–Liouville fractional integral of non-affine fractal interpolation function and its fractional operator
    T. M. C. Priyanka
    A. Gowrisankar
    The European Physical Journal Special Topics, 2021, 230 : 3789 - 3805
  • [29] An extension of Schweitzer's inequality to Riemann-Liouville fractional integral
    Abdeljawad, Thabet
    Meftah, Badreddine
    Lakhdari, Abdelghani
    Alqudah, Manar A.
    OPEN MATHEMATICS, 2024, 22 (01):
  • [30] Fractional Order Riemann-Liouville Integral Equations with Multiple Time Delays
    Abbas, Said
    Benchohra, Mouffak
    APPLIED MATHEMATICS E-NOTES, 2012, 12 : 79 - 87
12345