Normalized finite fractional differences: Computational and accuracy breakthroughs

Rafał Stanisławski; Krzysztof J. Latawiec

International Journal of Applied Mathematics and Computer Science (2012)

  • Volume: 22, Issue: 4, page 907-919
  • ISSN: 1641-876X

Abstract

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This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with the introduction of a perfect finite fractional difference and, in particular, a powerful adaptive finite fractional difference, whose excellent performance is illustrated in simulation examples.

How to cite

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Rafał Stanisławski, and Krzysztof J. Latawiec. "Normalized finite fractional differences: Computational and accuracy breakthroughs." International Journal of Applied Mathematics and Computer Science 22.4 (2012): 907-919. <http://eudml.org/doc/244564>.

@article{RafałStanisławski2012,
abstract = {This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with the introduction of a perfect finite fractional difference and, in particular, a powerful adaptive finite fractional difference, whose excellent performance is illustrated in simulation examples.},
author = {Rafał Stanisławski, Krzysztof J. Latawiec},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fractional difference; Grünwald-Letnikov difference; stability analysis; recursive computation; adaptive systems; adaptive systems.},
language = {eng},
number = {4},
pages = {907-919},
title = {Normalized finite fractional differences: Computational and accuracy breakthroughs},
url = {http://eudml.org/doc/244564},
volume = {22},
year = {2012},
}

TY - JOUR
AU - Rafał Stanisławski
AU - Krzysztof J. Latawiec
TI - Normalized finite fractional differences: Computational and accuracy breakthroughs
JO - International Journal of Applied Mathematics and Computer Science
PY - 2012
VL - 22
IS - 4
SP - 907
EP - 919
AB - This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with the introduction of a perfect finite fractional difference and, in particular, a powerful adaptive finite fractional difference, whose excellent performance is illustrated in simulation examples.
LA - eng
KW - fractional difference; Grünwald-Letnikov difference; stability analysis; recursive computation; adaptive systems; adaptive systems.
UR - http://eudml.org/doc/244564
ER -

References

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