Dimension of Riemann-Liouville fractional integral of Takagi function

In this paper, we mainly discuss the characteristics of a type of special function called Takagi function which was derived from Weierstrass function. We have proved this function is continuous but can not be differentiable on any subinterval. In other words, it has no bounded variation points even one. Then, we calculate its Hausdorff dimension and Box dimension is 1. Furthermore, its Riemann-Liouville fractional integral is also 1. Finally, some numerical and graphic results are provided to characterize Takagi function.