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Fractal dimension of Katugampola fractional integral of vector-valued functions

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Abstract

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 \(\mathbb {R}.\) 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.

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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical study and no experimental data has been listed.]

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005, India

    Megha Pandey & Tanmoy Som

  2. Department of Applied Sciences, Indian Institute of Information Technology Allahabad, Prayagraj, 211015, India

    Saurabh Verma

Authors
  1. Megha Pandey
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  2. Tanmoy Som
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  3. Saurabh Verma
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Pandey, M., Som, T. & Verma, S. Fractal dimension of Katugampola fractional integral of vector-valued functions. Eur. Phys. J. Spec. Top. 230, 3807–3814 (2021). https://doi.org/10.1140/epjs/s11734-021-00327-2

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  • DOI: https://doi.org/10.1140/epjs/s11734-021-00327-2

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