THE RELATIONSHIP BETWEEN FRACTAL DIMENSIONS OF BESICOVITCH FUNCTION AND THE ORDER OF HADAMARD FRACTIONAL INTEGRAL-Reference-Cited by-同舟云学术

THE RELATIONSHIP BETWEEN FRACTAL DIMENSIONS OF BESICOVITCH FUNCTION AND THE ORDER OF HADAMARD FRACTIONAL INTEGRAL

Published:2020-11 Issue:07 Volume:28 Page:2050128
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

WANG BIN¹,JI WENLONG²^ORCID,ZHANG LEGUI²,LI XUAN³

Affiliation:

1. College of Command and Control Engineering, Army Engineering University of PLA, Nanjing 211101, China

2. Department of Space System, Beijing 100094, China

3. National University of Defense Technology, Changsha 410000l, China

Abstract

In this paper, we mainly research on Hadamard fractional integral of Besicovitch function. A series of propositions of Hadamard fractional integral of [Formula: see text] have been proved first. Then, we give some fractal dimensions of Hadamard fractional integral of Besicovitch function including Box dimension, [Formula: see text]-dimension and Packing dimension. Finally, relationship between the order of Hadamard fractional integral and fractal dimensions of Besicovitch function has also been given.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X20501285

Reference17 articles.

1. On the fractional calculus of Besicovitch function

2. Fractional derivatives of Weierstrass-type functions

3. On a class of fractals: the constructive structure

4. The relationship between the fractal dimensions of a type of fractal functions and the order of their fractional calculus

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