On the approximate inverse Laplace transform of the transfer function with a single fractional order

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dc.authoridTan, Nusret/0000-0002-1285-1991
dc.authorwosidTan, Nusret/ABG-8122-2020
dc.contributor.authorYuce, Ali
dc.contributor.authorTan, Nusret
dc.date.accessioned2024-08-04T20:49:09Z
dc.date.available2024-08-04T20:49:09Z
dc.date.issued2021
dc.departmentİnönü Üniversitesien_US
dc.description.abstractThe history of fractional calculus dates back to 1600s and it is almost as old as classical mathematics. Although many studies have been published on fractional-order control systems in recent years, there is still a lack of analytical solutions. The focus of this study is to obtain analytical solutions for fractional order transfer functions with a single fractional element and unity coefficient. Approximate inverse Laplace transformation, that is, time response of the basic transfer function, is obtained analytically for the fractional order transfer functions with single-fractional-element by curve fitting method. Obtained analytical equations are tabulated for some fractional orders of alpha is an element of {0.1, 0.2, 0.3, ... , 0.9}. Moreover, a single function depending on fractional order alpha has been introduced for the first time using a table for 1=(s(alpha) + 1). By using this table, approximate inverse Laplace transform function is obtained in terms of any fractional order of a for 0 < alpha < 1. Obtained analytic equations offer accurate results in computing inverse Laplace transforms. The accuracy of the method is supported by numerical examples in this study. Also, the study sets the basis for the higher fractional-order systems that can be decomposed into a single (simpler) fractional order systems.en_US
dc.identifier.doi10.1177/0142331220977660
dc.identifier.endpage1384en_US
dc.identifier.issn0142-3312
dc.identifier.issn1477-0369
dc.identifier.issue6en_US
dc.identifier.scopus2-s2.0-85097958133en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage1376en_US
dc.identifier.urihttps://doi.org/10.1177/0142331220977660
dc.identifier.urihttps://hdl.handle.net/11616/99681
dc.identifier.volume43en_US
dc.identifier.wosWOS:000641865400010en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSage Publications Ltden_US
dc.relation.ispartofTransactions of The Institute of Measurement and Controlen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectFractional calculusen_US
dc.subjectinverse Laplace transformen_US
dc.subjectcurve fittingen_US
dc.subjectMittag-Leffler functionen_US
dc.subjectfractional order transfer functionsen_US
dc.titleOn the approximate inverse Laplace transform of the transfer function with a single fractional orderen_US
dc.typeArticleen_US

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