Rhapsody in fractional

Jose Tenreiro Machado; António Mendes Lopes; Fernando B.M. Duarte; Manuel Duarte Ortigueira; Raul Tello Rato

doi:10.2478/s13540-014-0206-0

Rhapsody in fractional

Jose Tenreiro Machado, António Mendes Lopes, Fernando B.M. Duarte, Manuel Duarte Ortigueira, Raul Tello Rato

Research output: Contribution to journal › Article

29 Citations (Scopus)

Abstract

This paper studies several topics related with the concept of “frac- tional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabil- ities, fractional delay discrete-time linear systems, and fractional Fourier transform.

Original language	English
Pages (from-to)	1188-1214
Journal	Fractional Calculus and Applied Analysis
Volume	17
Issue number	4
DOIs	https://doi.org/10.2478/s13540-014-0206-0
Publication status	Published - 2014

Keywords

difference equations
fractional delay
fractional Fourier transform
fractional sums
matrix power
matrix root
negative probability
positional number systems
tolerant computing

Access to Document

10.2478/s13540-014-0206-0

Fingerprint Dive into the research topics of 'Rhapsody in fractional'. Together they form a unique fingerprint.

Cite this

Machado, J. T., Lopes, A. M., Duarte, F. B. M., Ortigueira, M. D., & Rato, R. T. (2014). Rhapsody in fractional. Fractional Calculus and Applied Analysis, 17(4), 1188-1214. https://doi.org/10.2478/s13540-014-0206-0

@article{5ae0e99c62e047a3a3855098f1c2f76b,

title = "Rhapsody in fractional",

abstract = "This paper studies several topics related with the concept of “frac- tional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabil- ities, fractional delay discrete-time linear systems, and fractional Fourier transform.",

keywords = "tolerant computing, positional number systems, fractional Fourier transform, negative probability, fractional sums, matrix power, frac- tional delay, matrix root, difference equations, difference equations, fractional delay, fractional Fourier transform, fractional sums, matrix power, matrix root, negative probability, positional number systems, tolerant computing",

author = "Machado, {Jose Tenreiro} and Lopes, {Ant{\'o}nio Mendes} and Duarte, {Fernando B.M.} and Ortigueira, {Manuel Duarte} and Rato, {Raul Tello}",

note = "This work was partially supported by Instituto Politecnico de Setubal, by Universidade Nova de Lisboa, by Uninova-CTS, and by national funds by means of FCT - Fundacao para a Ciencia e a Tecnologia (project PEst-OE/EEI/UI0066/2011).",

year = "2014",

doi = "10.2478/s13540-014-0206-0",

language = "English",

volume = "17",

pages = "1188--1214",

journal = "Fractional Calculus and Applied Analysis",

issn = "1311-0454",

publisher = "WALTER DE GRUYTER GMBH",

number = "4",

}

TY - JOUR

T1 - Rhapsody in fractional

AU - Machado, Jose Tenreiro

AU - Lopes, António Mendes

AU - Duarte, Fernando B.M.

AU - Ortigueira, Manuel Duarte

AU - Rato, Raul Tello

N1 - This work was partially supported by Instituto Politecnico de Setubal, by Universidade Nova de Lisboa, by Uninova-CTS, and by national funds by means of FCT - Fundacao para a Ciencia e a Tecnologia (project PEst-OE/EEI/UI0066/2011).

PY - 2014

Y1 - 2014

N2 - This paper studies several topics related with the concept of “frac- tional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabil- ities, fractional delay discrete-time linear systems, and fractional Fourier transform.

AB - This paper studies several topics related with the concept of “frac- tional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabil- ities, fractional delay discrete-time linear systems, and fractional Fourier transform.

KW - tolerant computing

KW - positional number systems

KW - fractional Fourier transform

KW - negative probability

KW - fractional sums

KW - matrix power

KW - frac- tional delay

KW - matrix root

KW - difference equations

KW - fractional delay

KW - fractional Fourier transform

KW - fractional sums

KW - matrix power

KW - matrix root

KW - negative probability

KW - positional number systems

KW - tolerant computing

U2 - 10.2478/s13540-014-0206-0

DO - 10.2478/s13540-014-0206-0

M3 - Article

VL - 17

SP - 1188

EP - 1214

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

SN - 1311-0454

IS - 4

ER -