Box Dimension of Weyl Fractional Integral of Continuous Functions with Bounded Variation (Analysis in Theory and Applications, 2016)
We know that the Box dimension of $f(x)\in C^1[0,1]$ is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integral of above function is also 1.
Keywords: Fractional calculus; box dimension; bounded variation.