The Hausdorff dimension of Hadamard fractional integral of a fractal function

This paper mainly investigates the Hadamard fractional integral of the generalized Weierstrass function with random phases. We get the Hausdorff dimension of this type of fractal function by using potential theory and some classical methods. We show that there exists a linear connection between the Hausdorff dimension of this fractal function and the order of Hadamard fractional integral.