  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]X[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]X[0; 1] is still
two. Moreover, the results are also established for the mixed Hadamard
fractional integral.
