Basis Functions for a Transient Analysis of Linear Commensurate Fractional-Order Systems

Autor:	Dalibor Biolek, Viera Biolková, Zdeněk Kolka, Zdeněk Biolek
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	Mittag–Leffler function commensurate fractional-order system basis function impulse response Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
Zdroj:	Algorithms, Vol 16, Iss 7, p 335 (2023)
Druh dokumentu:	article
ISSN:	1999-4893
DOI:	10.3390/a16070335
Popis:	In this paper, the possibilities of expressing the natural response of a linear commensurate fractional-order system (FOS) as a linear combination of basis functions are analyzed. For all possible types of sα-domain poles, the corresponding basis functions are found, the kernel of which is the two-parameter Mittag–Leffler function Eα,β, β = α. It is pointed out that there are mutually unambiguous correspondences between the basis functions of FOS and the known basis functions of the integer-order system (IOS) for α = 1. This correspondence can be used to algorithmically find analytical formulas for the impulse responses of FOS when the formulas for the characteristics of IOS are known. It is shown that all basis functions of FOS can be generated with Podlubny‘s function of type εk (t, c; α, α), where c and k are the corresponding pole and its multiplicity, respectively.
Databáze:	Directory of Open Access Journals
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