TY - JOUR
T1 - An Operational Approach to Fractional Scale-Invariant Linear Systems
AU - Bengochea, Gabriel
AU - Ortigueira, Manuel Duarte
N1 - Funding Information:
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00066%2F2020/PT#
Publisher Copyright:
© 2023 by the authors.
PY - 2023/7/2
Y1 - 2023/7/2
N2 - The fractional scale-invariant systems are introduced and studied, using an operational formalism. It is shown that the impulse and step responses of such systems belong to the vector space generated by some special functions here introduced. For these functions, the fractional scale derivative is a decremental index operator, allowing the construction of an algebraic framework that enables to compute the impulse and step responses of such systems. The effectiveness and accuracy of the method are demonstrated through various numerical simulations.
AB - The fractional scale-invariant systems are introduced and studied, using an operational formalism. It is shown that the impulse and step responses of such systems belong to the vector space generated by some special functions here introduced. For these functions, the fractional scale derivative is a decremental index operator, allowing the construction of an algebraic framework that enables to compute the impulse and step responses of such systems. The effectiveness and accuracy of the method are demonstrated through various numerical simulations.
KW - fractional scale derivative
KW - fractional scale-invariant
KW - hadamard derivative
KW - Mellin transform
KW - operational calculus
KW - stretching derivative
UR - http://www.scopus.com/inward/record.url?scp=85165995331&partnerID=8YFLogxK
U2 - 10.3390/fractalfract7070524
DO - 10.3390/fractalfract7070524
M3 - Article
AN - SCOPUS:85165995331
SN - 2504-3110
VL - 7
JO - Fractal and Fractional
JF - Fractal and Fractional
IS - 7
M1 - 524
ER -