FRACTAL DIMENSION OF RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL OF CERTAIN UNBOUNDED VARIATIONAL CONTINUOUS FUNCTION

In the present paper, a one-dimensional continuous function of unbounded variation on the interval [0, 1] has been constructed. Box dimension of this function has been proved to be 1. Furthermore, Box dimension of its Riemann–Liouville fractional integral of any order has also been proved to be 1.