Abstract
AbstractThe 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.
Funder
Fundação para a Ciência e a Tecnologia
Universidade Nova de Lisboa
Publisher
Springer Science and Business Media LLC
Reference56 articles.
1. Abel, N.: Auflösung einer mechanischen aufgabe. Journal für die reine und angewandte Mathematik (Crelle) 1, 153–157 (1826). https://doi.org/10.1515/crll.1826.1.153
2. Abel, N.H.: Oplösning af et par opgaver ved hjelp af bestemte integraler. Magazin for naturvidenskaberne 2(55), 2 (1823)
3. Abel, N.H.: Œuvres complètes de Niels Henrik Abel, vol. 1. Grøndahl (1881)
4. Bengochea, G., Ortigueira, M., Verde-Star, L.: The causal $$\alpha $$-exponential and the solution of fractional linear time-invariant systems. International Journal of Systems Science 55(9), 1790–1806 (2024)
5. Chaudhry, M.A., Zubair, S.M.: On a Class of Incomplete Gamma Functions with Applications. Chapman and Hall/CRC (2001)
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