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- W3214806207 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." @default.
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- W3214806207 date "2021-11-30" @default.
- W3214806207 modified "2023-10-04" @default.
- W3214806207 title "Fractal dimension of Katugampola fractional integral of vector-valued functions" @default.
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- W3214806207 doi "https://doi.org/10.1140/epjs/s11734-021-00327-2" @default.
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