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Mathematical Problems in Engineering
Volume 2014, Article ID 737694, 11 pages
http://dx.doi.org/10.1155/2014/737694
Review Article

Fractal-Based Methods and Inverse Problems for Differential Equations: Current State of the Art

1Department of Mathematics and Statistics, University of Guelph, Guelph, ON, Canada N1G 2W1
2Department of Economics, Management, and Quantitative Methods, University of Milan, 20122 Milan, Italy
3Department of Applied Mathematics and Sciences, Khalifa University, P.O. Box 127788, Abu Dhabi, UAE
4Department of Mathematics and Statistics, Acadia University, Wolfville, NS, Canada B4P 2R6
5Department of Applied Mathematics, University of Granada, 18071 Granada, Spain

Received 18 March 2014; Accepted 30 July 2014; Published 20 November 2014

Academic Editor: Asier Ibeas

Copyright © 2014 Herb E. Kunze et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We illustrate, in this short survey, the current state of the art of fractal-based techniques and their application to the solution of inverse problems for ordinary and partial differential equations. We review several methods based on the Collage Theorem and its extensions. We also discuss two innovative applications: the first one is related to a vibrating string model while the second one considers a collage-based approach for solving inverse problems for partial differential equations on a perforated domain.