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

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.