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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 795954, 7 pages
http://dx.doi.org/10.1155/2013/795954
Research Article

On Generalized Fractional Differentiator Signals

1Faculty of Computer Science and Information Technology, University Malaya, 50603 Kuala Lumpur, Malaysia
2Institute of Mathematical Sciences, University Malaya, 50603 Kuala Lumpur, Malaysia

Received 17 January 2013; Accepted 16 March 2013

Academic Editor: Jehad Alzabut

Copyright © 2013 Hamid A. Jalab and Rabha W. Ibrahim. 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

By employing the generalized fractional differential operator, we introduce a system of fractional order derivative for a uniformly sampled polynomial signal. The calculation of the bring in signal depends on the additive combination of the weighted bring-in of cascaded digital differentiators. The weights are imposed in a closed formula containing the Stirling numbers of the first kind. The approach taken in this work is to consider that signal function in terms of Newton series. The convergence of the system to a fractional time differentiator is discussed.