Box dimensions of Riemann–Liouville fractional integrals of continuous functions of bounded variation Original Research Article

If a continuous function f(x)f(x) has bounded variation on the unit interval [0,1][0,1], the box dimension of f(x)f(x) is 1. Furthermore, the box dimension of a Riemann–Liouville fractional integral of f(x)f(x) is still 1.