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] × [0, 1]. We prove that the box dimension of the mixed Katugampola fractional integral having fractional order (α = (α1, α2); α1 > 0, α2 > 0) of two-dimensional continuous functions on [0, 1] × [0, 1] is still two. Moreover, the results are also established for the mixed Hadamard fractional integral.