Derivation of analytical inverse Laplace transform for fractional order integrator

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dc.authorscopusid56448379000
dc.authorscopusid7202696962
dc.contributor.authorYücef A.
dc.contributor.authorTan N.
dc.date.accessioned2024-08-04T20:03:37Z
dc.date.available2024-08-04T20:03:37Z
dc.date.issued2017
dc.departmentİnönü Üniversitesien_US
dc.description.abstractThere is considerable interest in the study of fractional order deriva- tive/integrator but obtaining analytical impulse and step responses is a difficult problem. Therefore all methods reported on to date use approximations for the fractional derivative/integrator both for an- alytical based computations and more relevantly in simulation stud- ies. In this paper, an analytical formula is first derived for the in- verse Laplace transform of fractional order integrator, 1/s? where ? ? R and 0 < ? <1 using Stirling's formula and Gamma func- tion. Then, the analytical step response of fractional integrator has been computed from the derived impulse response of 1/s?. The ob- tained analytical formulas for impulse and step responses of frac- tional order integrator are exact results except the very small error due to the neglected terms of Stirling's series. The results are com- pared with some well known integer order approximation methods and Grunwald-Letnikov (GL) approximation technique. It has been shown via numerical examples that the presented method is very suc- cessful according to other methods. © 2017 L&H Scientific Publishing, LLC.en_US
dc.identifier.doi10.5890/JAND.2017.06.013
dc.identifier.endpage314en_US
dc.identifier.issn2164-6457
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-85020888299en_US
dc.identifier.scopusqualityQ4en_US
dc.identifier.startpage303en_US
dc.identifier.urihttps://doi.org/10.5890/JAND.2017.06.013
dc.identifier.urihttps://hdl.handle.net/11616/91944
dc.identifier.volume6en_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherL and H Scientific Publishing, LLCen_US
dc.relation.ispartofJournal of Applied Nonlinear Dynamicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectConvolution integralen_US
dc.subjectFractional order integratoren_US
dc.subjectGamma functionen_US
dc.subjectLaplace transformen_US
dc.subjectStirling's formulaen_US
dc.titleDerivation of analytical inverse Laplace transform for fractional order integratoren_US
dc.typeArticleen_US

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