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]X[0; 1]. We prove that the box dimension of the mixed Katugampola fractional integral having fractional order (α= (α_1; α_2); α_1 > 0; α_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.

10 pages. Submitted in a journal