Upper Bound Estimation of Fractal Dimension of Fractional Calculus of Continuous Functions

Abstract

In the present paper, upper bound estimation of upper Box dimension of RiemannLiouville fractional integral of order v of any continuous functions on a closed interval has been proved to be no more than 2 − v when 0 < v < 1. If a continuous function which satisfies α-Hölder condition on a closed interval, upper Box dimension of its Riemann-Liouville fractional integral is no more than 2 − α when 0 < α < 1. Upper bound of upper Box dimension of Riemann-Liouivlle fractional integral of certain type of fractal functions has been proved to be no more than Box dimension of functions themselves.