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- Title
Fractal dimension of Katugampola fractional integral of vector-valued functions.
- Authors
Pandey, Megha; Som, Tanmoy; Verma, Saurabh
- 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 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.
- Subjects
FRACTAL dimensions; INTEGRAL functions; FUNCTIONS of bounded variation; GRAPH theory; HOLDER spaces; CONTINUOUS functions; FRACTAL analysis
- Publication
European Physical Journal: Special Topics, 2021, Vol 230, Issue 21/22, p3807
- ISSN
1951-6355
- Publication type
Article
- DOI
10.1140/epjs/s11734-021-00327-2