TY - JOUR
T1 - Discrete-Time Fractional Difference Calculus
T2 - Origins, Evolutions, and New Formalisms
AU - Ortigueira, Manuel Duarte
N1 - Funding Information:
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00066%2F2020/PT#
Publisher Copyright:
© 2023 by the author.
PY - 2023/6/25
Y1 - 2023/6/25
N2 - Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time differences are described. ARMA-type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown.
AB - Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time differences are described. ARMA-type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown.
KW - ARFIMA
KW - ARMA
KW - bilateral difference
KW - bilinear
KW - delta difference
KW - nabla difference
KW - stretching difference
KW - tempered
UR - http://www.scopus.com/inward/record.url?scp=85166010189&partnerID=8YFLogxK
U2 - 10.3390/fractalfract7070502
DO - 10.3390/fractalfract7070502
M3 - Article
AN - SCOPUS:85166010189
SN - 2504-3110
VL - 7
JO - Fractal and Fractional
JF - Fractal and Fractional
IS - 7
M1 - 502
ER -