Fractal dimension of Hadamard fractional integral of continuous functions with countable UV points

The present paper investigates fractal dimension of Hadamard fractional integral of continuous functions with countable UV points. Firstly, we prove that fractal dimension of Hadamard fractional integral of continuous functions with at most one UV point is 1. More generally, the conclusion still holds for continuous function containing finite UV points. Furthermore, we show that Hausdorff dimension of Hadamard fractional integral of continuous functions containing coutable UV points is 1. Finally, Box dimension of Hadamard fractional integral of continuous functions containing coutable UV points has been given.