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Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions

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Abstract

The goal of this article is to study the box dimension of the mixed Katugampola fractional integral of two-dimensional continuous functions on \([0,1]\times [0,1]\). We prove that the box dimension of the mixed Katugampola fractional integral having fractional order \((\alpha =(\alpha _1,\alpha _2);~ \alpha _1>0, \alpha _2>0)\) of two-dimensional continuous functions on \([0,1]\times [0,1]\) is still two. Moreover, the results are also established for the mixed Hadamard fractional integral. Our new results are to improve the existing studies. We pose also some open problems for further research.

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Acknowledgements

We are thankful to the handling editor and anonymous reviewers for their constructive comments and suggestions, which helped us to improve the manuscript. The first author thanks to CSIR, India for the financial support (Grant No: 09/1058(0012) /2018-EMR-I).

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  1. School of Basic Sciences, Indian Institute of Technology Mandi, Kamand, HP, 175005, India

    Subhash Chandra & Syed Abbas

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  1. Subhash Chandra
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  2. Syed Abbas
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Correspondence to Syed Abbas.

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Chandra, S., Abbas, S. Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions. Fract Calc Appl Anal 25, 1022–1036 (2022). https://doi.org/10.1007/s13540-022-00050-2

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