TY - JOUR
T1 - Searching for Sonin kernels
AU - Ortigueira, Manuel D.
N1 - Funding Information:
info:eu-repo/grantAgreement/FCT/Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017%2F2018) - Financiamento Base/UIDB%2F00066%2F2020/PT#
Publisher Copyright:
© The Author(s) 2024.
PY - 2024/10
Y1 - 2024/10
N2 - The causal shift-invariant convolution is studied from the point of view of inversion. Abel’s algorithm, used in the tautochrone problem, is considered and Sonin’s existence condition is deduced. To generate pairs of functions verifying Sonin’s condition, the class of Mittag-Leffler type functions is used. In particular, functions that are impulse responses of ARMA(N,N) systems serve as a basis. The possible use of Abel’s procedure as a support for introducing generalized fractional derivatives is evaluated.
AB - The causal shift-invariant convolution is studied from the point of view of inversion. Abel’s algorithm, used in the tautochrone problem, is considered and Sonin’s existence condition is deduced. To generate pairs of functions verifying Sonin’s condition, the class of Mittag-Leffler type functions is used. In particular, functions that are impulse responses of ARMA(N,N) systems serve as a basis. The possible use of Abel’s procedure as a support for introducing generalized fractional derivatives is evaluated.
KW - 26A33
KW - 26A36
KW - 42A85 (primary)
KW - 45E10
KW - Almost regular function
KW - Convolution (primary)
KW - Fractional calculus
KW - Generalized fractional derivative
KW - Sonin kernel
UR - http://www.scopus.com/inward/record.url?scp=85200694950&partnerID=8YFLogxK
U2 - 10.1007/s13540-024-00321-0
DO - 10.1007/s13540-024-00321-0
M3 - Article
AN - SCOPUS:85200694950
SN - 1311-0454
VL - 27
SP - 2219
EP - 2247
JO - Fractional Calculus and Applied Analysis
JF - Fractional Calculus and Applied Analysis
IS - 5
ER -