Article
On the relationship between the Hausdorff dimension and the integration order.
USF St. Petersburg campus Faculty Publications
Document Type
Article
Publication Date
2007
Disciplines
Abstract
We use the Grűnwald definition for the integration of the function f : [0, 1] → R to construct an iterated function system on the interval [0, 1]. Then we show that this iterated function system satisfies the open set condition. Using this construction, we further show that the Hausdorff dimension is intimately related to the order of the fractional integration process for any real order q > 0.
Comments
Abstract only. Full-text article is available only through licensed access provided by the publisher. Published in Journal of Mathematics, Statistics and Allied Fields, 1(2)
Language
en_US
Publisher
Scientific Journals International
Creative Commons License
Creative Commons Attribution-Noncommercial-No Derivative Works 4.0
Citation Information
Hardy, L.C. (2007). On the relationship between the Hausdorff dimension and the integration order. Journal of Mathematics, Statistics and Allied Fields, 1(2)