A NOTE ON FRACTAL DIMENSION OF RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL

Subhash Chandra (), Syed Abbas and Yongshun Liang ()
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Subhash Chandra: School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, Kamand 175005, Himachal Pradesh India
Syed Abbas: School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, Kamand 175005, Himachal Pradesh India
Yongshun Liang: Institute of Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 02, 1-14

Abstract: This paper intends to study the analytical properties of the Riemann–Liouville fractional integral and fractal dimensions of its graph on ℠n. We show that the Riemann–Liouville fractional integral preserves some analytical properties such as boundedness, continuity and bounded variation in the Arzelá 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 Hölder 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 Arzelá sense, are n.

Keywords: Riemann–Liouville Fractional Integral; Bounded Variation; Box Dimension; Hausdorff Dimension (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400012

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