Box Dimension of Mixed Katugampola Fractional Integral of Two-Dimensional Continuous Functions

TL;DR

This paper investigates the fractal dimension of the mixed Katugampola fractional integral of two-dimensional continuous functions, establishing that the dimension remains two, and extends results to the mixed Hadamard fractional integral.

Contribution

It proves that the box dimension of the mixed Katugampola fractional integral of 2D continuous functions remains two, and extends the analysis to the mixed Hadamard fractional integral.

Findings

Box dimension of the fractional integral is two.

Results apply to both Katugampola and Hadamard fractional integrals.

Dimension preservation under fractional integration for 2D 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 (\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.