Analysis of fractal dimension of mixed Riemann-Liouville integral

In this article, we provide a rigorous study on the fractal dimension of the graph of the mixed Riemann-Liouville fractional integral for various choices of continuous functions on a rectangular region. We estimate bounds for the box dimension and the Hausdorff dimension of the graph of the mixed Ri...

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Bibliographic Details
Published in:Numerical algorithms Vol. 91; no. 3; pp. 1021 - 1046
Main Authors: Chandra, Subhash, Abbas, Syed
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2022
Springer Nature B.V
Subjects:
Algebra
Algorithms
Calculus
Computer Science
Continuity (mathematics)
Fractal analysis
Fractal geometry
Fractals
Fractional calculus
Integrals
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
26A30
Hausdorff dimension
Riemann-Liouville fractional integral
Bounded variation
26A33
28A78
28A80
Box dimension
Hölder condition
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In this article, we provide a rigorous study on the fractal dimension of the graph of the mixed Riemann-Liouville fractional integral for various choices of continuous functions on a rectangular region. We estimate bounds for the box dimension and the Hausdorff dimension of the graph of the mixed Riemann-Liouville fractional integral of the functions which belong to the class of continuous functions and the class of Hölder continuous functions. We also show that the box dimension of the graph of the mixed Riemann-Liouville fractional integral of two-dimensional continuous functions is also two. Furthermore, we give the construction of unbounded variational continuous functions. Later, we prove that the box dimension and the Hausdorff dimension of the graph of the mixed Riemann-Liouville fractional integral of unbounded variational continuous functions are two. Moreover, we illustrate our results by using some examples.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01290-2