# 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

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topRafał 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 -

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