Affiliation:
1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
Abstract
In this paper, we will prove two properties for the Riemann–Liouville fractal derivatives and integrals, respectively. One is that if [Formula: see text] is a Lipschitz function, then [Formula: see text] is [Formula: see text]th-order differentiable almost everywhere in the Riemann–Liouville sense for any [Formula: see text]. The other is that if the Box dimension for a continuous function [Formula: see text] is one, then for any [Formula: see text], the Box dimension of [Formula: see text] is also one. We also give an example to show that there exists a rectifiable function [Formula: see text], but for any [Formula: see text], [Formula: see text], the Riemann–Liouville fractal integral of [Formula: see text], is rectifiable.
Funder
National Natural Science Foundation of China
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation