Fractal dimension of Katugampola fractional integral of vector-valued functions

Calculating fractal dimension of the graph of a function not simple even for real-valued functions. While through this paper, our intention is to provide some initial theories for the dimension of the graphs of vector-valued functions. In particular, we give a fresh attempt to estimate the fractal d...

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Bibliographic Details
Published in:The European physical journal. ST, Special topics Special topics, 2021-12, Vol.230 (21-22), p.3807-3814
Main Authors: Pandey, Megha, Som, Tanmoy, Verma, Saurabh
Format: Article
Language:English
Subjects:
Atomic
Classical and Continuum Physics
Condensed Matter Physics
Continuity (mathematics)
Fractal geometry
Fractals
Fractional calculus
Frontiers of Fractals for Complex Systems: Recent Advances and Future Challenges
Materials Science
Mathematical analysis
Mathematical functions
Measurement Science and Instrumentation
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
Upper bounds
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Summary:Calculating fractal dimension of the graph of a function not simple even for real-valued functions. While through this paper, our intention is to provide some initial theories for the dimension of the graphs of vector-valued functions. In particular, we give a fresh attempt to estimate the fractal dimension of the graph of the Katugampola fractional integral of a vector-valued continuous function of bounded variation defined on a closed bounded interval in R . We prove that dimension of the graph of a continuous vector-valued function of bounded variation is 1 and so is the dimension of the graph of its Katugampola fractional integral. Further, for a Hölder continuous function, we provide an upper bound for the upper box dimension of the graph of each coordinate function of the Katugampola fractional integral of the function.
ISSN:1951-6355
1951-6401
DOI:10.1140/epjs/s11734-021-00327-2