Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 732917, 21 pages
Research Article

New Laguerre Filter Approximators to the Grünwald-Letnikov Fractional Difference

Institute of Control and Computer Engineering, Opole University of Technology, ul. Proszkowska 76, 45-758 Opole, Poland

Received 9 September 2012; Accepted 16 November 2012

Academic Editor: Alex Elias-Zuniga

Copyright © 2012 Rafał Stanisławski. 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.


This paper presents a series of new results in modeling of the Grünwald-Letnikov discrete-time fractional difference by means of discrete-time Laguerre filers. The introduced Laguerre-based difference (LD) and combined fractional/Laguerre-based difference (CFLD) are shown to perfectly approximate its fractional difference original, for fractional order . This paper is culminated with the presentation of finite (combined) fractional/Laguerre-based difference (FFLD), whose excellent approximation performance is illustrated in simulation examples.