Fractal dimensions of mixed Katugampola fractional integral associated with vector valued functions

Subhash Chandra and Syed Abbas

Chaos, Solitons & Fractals, 2022, vol. 164, issue C

Abstract: The aim of this article is to study the fundamental properties of the mixed Katugampola fractional integral (K-integral) of vector-valued functions and fractal dimensional results. We show that the mixed K-integral preserves the basic properties such as boundedness, continuity, and bounded variation of vector-valued functions. We also estimate the Hausdorff dimension of the graph of the vector-valued function and the graph of the mixed K-integral on the rectangular region. Moreover, we prove that the upper bound of the box dimension of the graph of each coordinate function of mixed K-integral of vector-valued functions is 3−min{μ1,μ2}, where μ1 and μ2 are order of the fractional integral with 0<μ1<1,0<μ2<1. Moreover, we give an example of unbounded variational vector-valued functions. In the end, we discuss some problems for future direction.

Keywords: Katugampola fractional integral; Fractal dimension; Bounded variation; Hölder condition (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:164:y:2022:i:c:s096007792200827x

DOI: 10.1016/j.chaos.2022.112648

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