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dc.contributor.authorLiu, Dayan
dc.contributor.authorLaleg-Kirati, Taous-Meriem
dc.contributor.authorGibaru, O.
dc.date.accessioned2015-08-11T13:44:05Z
dc.date.available2015-08-11T13:44:05Z
dc.date.issued2013-02-24
dc.identifier.isbn9783902823274
dc.identifier.issn14746670
dc.identifier.doi10.3182/20130204-3-FR-4032.00208
dc.identifier.urihttp://hdl.handle.net/10754/565865
dc.description.abstractIn this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method. © 2013 IFAC.
dc.publisherElsevier BV
dc.subjectDifferential equations
dc.subjectDifferentiators
dc.subjectParameter estimation
dc.titleFractional order differentiation by integration: An application to fractional linear systems
dc.typeConference Paper
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputational Bioscience Research Center (CBRC)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentElectrical Engineering Program
dc.identifier.journalIFAC Proceedings Volumes
dc.conference.date4 February 2013 through 6 February 2013
dc.conference.name6th Workshop on Fractional Differentiation and Its Applications, FDA 2013
dc.conference.locationGrenoble
kaust.personLiu, Dayan
kaust.personLaleg-Kirati, Taous-Meriem
dc.date.published-online2013-02-24
dc.date.published-print2013-02


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