Novel Fractional-Order Difference Schemes Reducible to Standard Integer-Order Formulas

In this letter, we advise numerical schemes for calculation of fractional derivatives of Grünwald-Letnikov type that reduce to standard integer-order derivative schemes. Since, in the literature, only forward differences have such a property, here, novel forms of backward differences and central di...

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Bibliographic Details
Published in:IEEE signal processing letters 2017-06, Vol.24 (6), p.912-916
Main Authors: Paskas, Milorad P., Reljin, Irini S., Reljin, Branimir D.
Format: Article
Language:English
Subjects:
Backward fractional differences
central fractional differences
Fourier transforms
fractional calculus
Grünwald–Letnikov derivatives
Image segmentation
Laplace equations
Mathematical model
texture enhancement
Transfer functions
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Summary:In this letter, we advise numerical schemes for calculation of fractional derivatives of Grünwald-Letnikov type that reduce to standard integer-order derivative schemes. Since, in the literature, only forward differences have such a property, here, novel forms of backward differences and central differences based both on integer and half-integer mesh points are proposed. It enables the use of the proposed fractional differences interchangeably with standard difference formulas. The proposed schemes are qualitatively and quantitatively tested on 2-D signals for texture enhancement. The obtained results show that the proposed fractional differences provide better performances in comparison to traditional schemes.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2017.2699285