Fractal dimension of graph of Katugampola fractional integral and some general characterizations

In this paper, we make research on Katugampola and Hadamard fractional integral of one-dimensional continuous functions on [Formula: see text]. We proved that Katugampola fractional integral of bounded and continuous function still is bounded and continuous. Box dimension of any positive order Hadamard fractional integral of one-dimensional continuous functions is one.

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FRACTAL DIMENSION OF A SPECIAL CONTINUOUS FUNCTION

Fractals ◽

10.1142/s0218348x18500482 ◽

2018 ◽

Vol 26 (04) ◽

pp. 1850048 ◽

Cited By ~ 1

Author(s):

NING LIU ◽

KUI YAO

Keyword(s):

Fractal Dimension ◽

Continuous Function ◽

Hausdorff Dimension ◽

Fractional Integral ◽

Fractal Function

In this paper, we mainly construct a special fractal function defined on [Formula: see text] of unbounded variation by method of iteration, and prove that both Box and Hausdorff dimension of this function be 1. Further, we discuss the Riemann–Liouville fractional integral of this function. Finally, some numerical and graphic results are provided to characterize this special fractal function.

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Hermite-Hadamard-Fejér type inequalities for co-ordinated harmonically convex functions via Katugampola fractional integrals

Engineering and Applied Science Letters ◽

10.30538/psrp-easl2021.0067 ◽

2021 ◽

Vol 4 (2) ◽

pp. 12-28

Author(s):

Naila Mehreen ◽

◽

Matloob Anwar ◽

Keyword(s):

Convex Functions ◽

Fractional Integral ◽

Fractional Integrals ◽

One Dimension ◽

Harmonically Convex Functions ◽

Katugampola Fractional Integral

The aim of this paper is to establish the Hermite-Hadamard-Fejér type inequalities for co-ordinated harmonically convex functions via Katugampola fractional integral. We provide Hermite-Hadamard-Fejér inequalities for harmonically convex functions via Katugampola fractional integral in one dimension.

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Further Discussion on Relationship between Fractal Dimension of Weierstrass Function and Order of Riemann-Liouville Fractional Integral

Pure Mathematics ◽

10.12677/pm.2020.1011123 ◽

2020 ◽

Vol 10 (11) ◽

pp. 1035-1043

Author(s):

鸿博高

Keyword(s):

Fractal Dimension ◽

Fractional Integral ◽

Weierstrass Function

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ESTIMATION OF FRACTAL DIMENSION OF WEYL FRACTIONAL INTEGRAL OF CERTAIN CONTINUOUS FUNCTIONS

Fractals ◽

10.1142/s0218348x20500309 ◽

2020 ◽

Vol 28 (02) ◽

pp. 2050030 ◽

Cited By ~ 1

Author(s):

YONG-SHUN LIANG

Keyword(s):

Fractal Dimension ◽

Fractional Integral ◽

Continuous Functions ◽

Box Dimension ◽

Hölder Condition ◽

Positive Order ◽

Weyl Fractional Integral

In this work, we consider fractal dimension such as Box dimension, of Weyl fractional integral of certain continuous functions. Upper Box dimension of Weyl fractional integral of continuous functions satisfying [Formula: see text]-order Hölder condition of positive order [Formula: see text] is no more than both [Formula: see text] and [Formula: see text]. Furthermore, it is no more than [Formula: see text] which means strictly less than [Formula: see text]. Meanwhile, [Formula: see text], Box dimension of Weyl fractional integral of continuous functions satisfying [Formula: see text]-order Hölder condition must be one.

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FRACTAL DIMENSION OF RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL OF CERTAIN UNBOUNDED VARIATIONAL CONTINUOUS FUNCTION

Fractals ◽

10.1142/s0218348x17500475 ◽

2017 ◽

Vol 25 (05) ◽

pp. 1750047 ◽

Cited By ~ 5

Author(s):

YANG LI ◽

WEI XIAO

Keyword(s):

Fractal Dimension ◽

Continuous Function ◽

Fractional Integral ◽

Box Dimension ◽

One Dimensional

In the present paper, a one-dimensional continuous function of unbounded variation on the interval [Formula: see text] has been constructed. Box dimension of this function has been proved to be 1. Furthermore, Box dimension of its Riemann–Liouville fractional integral of any order has also been proved to be 1.

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