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

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