TY - JOUR
T1 - Substantial, tempered, and shifted fractional derivatives
T2 - Three faces of a tetrahedron
AU - Ortigueira, Manuel D.
AU - Bengochea, Gabriel
AU - Machado, J. Tenreiro
N1 - info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00066%2F2020/PT#
PI-CCyT-2019-15
PY - 2021/7/30
Y1 - 2021/7/30
N2 - The substantial, tempered, and shifted fractional derivatives, useful in medium range systems, are reviewed and highlighted in a unified framework. Their historical evolution is described and their properties studied. Moreover, they are characterized and assessed under the light of the strict sense criterion for the definition of derivatives. The relationship between these derivatives and several formulations developed in fractional calculus are explored. Additionally, the interpretations in the time and frequency domains are included. In the scope of the framework, new tempered linear systems and transfer functions are introduced. As particular applications, several systems for compensation and control purposes are revisited.
AB - The substantial, tempered, and shifted fractional derivatives, useful in medium range systems, are reviewed and highlighted in a unified framework. Their historical evolution is described and their properties studied. Moreover, they are characterized and assessed under the light of the strict sense criterion for the definition of derivatives. The relationship between these derivatives and several formulations developed in fractional calculus are explored. Additionally, the interpretations in the time and frequency domains are included. In the scope of the framework, new tempered linear systems and transfer functions are introduced. As particular applications, several systems for compensation and control purposes are revisited.
KW - shifted fractional derivative
KW - substantial fractional derivative
KW - tempered fractional derivative
KW - tempered fractional system
UR - http://www.scopus.com/inward/record.url?scp=85103673301&partnerID=8YFLogxK
U2 - 10.1002/mma.7343
DO - 10.1002/mma.7343
M3 - Article
AN - SCOPUS:85103673301
SN - 0170-4214
VL - 44
SP - 9191
EP - 9209
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 11
ER -