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Mathematics 2015, 3(2), 487-509;

The Fractional Orthogonal Difference with Applications

Kooikersdreef 620, 7328 BS Apeldoorn, The Netherlands
Academic Editor: Hari M. Srivastava
Received: 4 March 2015 / Revised: 3 June 2015 / Accepted: 4 June 2015 / Published: 12 June 2015
(This article belongs to the Special Issue Recent Advances in Fractional Calculus and Its Applications)
Full-Text   |   PDF [302 KB, uploaded 12 June 2015]


This paper is a follow-up of a previous paper of the author published in Mathematics journal in 2015, which treats the so-called continuous fractional orthogonal derivative. In this paper, we treat the discrete case using the fractional orthogonal difference. The theory is illustrated with an application of a fractional differentiating filter. In particular, graphs are presented of the absolutel value of the modulus of the frequency response. These make clear that for a good insight into the behavior of a fractional differentiating filter, one has to look for the modulus of its frequency response in a log-log plot, rather than for plots in the time domain. View Full-Text
Keywords: orthogonal difference; orthogonal polynomials; hypergeometric functions; Fourier transform; frequency response orthogonal difference; orthogonal polynomials; hypergeometric functions; Fourier transform; frequency response
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 (CC BY 4.0).

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Diekema, E. The Fractional Orthogonal Difference with Applications. Mathematics 2015, 3, 487-509.

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