GENERAL FRACTAL DIMENSIONS OF GRAPHS OF CONTINUOUS FUNCTIONS ASSOCIATED WITH THE KATUGAMPOLA FRACTIONAL INTEGRAL

Abstract

This paper makes an investigation on graphs of continuous functions and their Katugampola fractional integral in terms of general fractal dimensions. Under certain circumstances, general fractal dimensions of continuous functions satisfying the Hölder condition and one-dimensional continuous functions have been discussed. On this basis, the corresponding results for their Katugampola fractional integral have also been presented. It has been shown that the previous conclusions regarding the original box dimension of fractional integral of continuous functions are still applicable to the new general box dimension. In addition, several specific examples have been provided to elaborate these theoretical findings. This work can be a typical case of applying general fractal dimensions to graphs of functions.