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.