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
VL - 17
SP - 1188
EP - 1214
JO - Fractional Calculus and Applied Analysis
JF - Fractional Calculus and Applied Analysis
SN - 1311-0454
IS - 4
ER -