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The Fractional Orthogonal Difference with Applications

Kooikersdreef 620, 7328 BS Apeldoorn, The Netherlands
Academic Editor: Hari M. Srivastava
Mathematics 2015, 3(2), 487-509; https://doi.org/10.3390/math3020487
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)
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
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MDPI and ACS Style

Diekema, E. The Fractional Orthogonal Difference with Applications. Mathematics 2015, 3, 487-509. https://doi.org/10.3390/math3020487

AMA Style

Diekema E. The Fractional Orthogonal Difference with Applications. Mathematics. 2015; 3(2):487-509. https://doi.org/10.3390/math3020487

Chicago/Turabian Style

Diekema, Enno. 2015. "The Fractional Orthogonal Difference with Applications" Mathematics 3, no. 2: 487-509. https://doi.org/10.3390/math3020487

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