Next Article in Journal
Effective Summation and Interpolation of Series by Self-Similar Root Approximants
Next Article in Special Issue
Time Automorphisms on C*-Algebras
Previous Article in Journal
The Complement of Binary Klein Quadric as a Combinatorial Grassmannian
Previous Article in Special Issue
Sinc-Approximations of Fractional Operators: A Computing Approach
Article Menu

Export Article

Open AccessArticle
Mathematics 2015, 3(2), 487-509; doi:10.3390/math3020487

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)
View Full-Text   |   Download PDF [302 KB, uploaded 12 June 2015]   |  

Abstract

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).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top