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 - 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

SN - 1311-0454

VL - 17

SP - 1188

EP - 1214

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

IS - 4

ER -