Fractional order differentiation by integration: An application to fractional linear systems

Handle URI:
http://hdl.handle.net/10754/565865
Title:
Fractional order differentiation by integration: An application to fractional linear systems
Authors:
Liu, Dayan; Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 ) ; Gibaru, O.
Abstract:
In 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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Elsevier BV
Journal:
IFAC Proceedings Volumes
Conference/Event name:
6th Workshop on Fractional Differentiation and Its Applications, FDA 2013
Issue Date:
4-Feb-2013
DOI:
10.3182/20130204-3-FR-4032.00208
Type:
Conference Paper
ISSN:
14746670
ISBN:
9783902823274
Appears in Collections:
Conference Papers; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLiu, Dayanen
dc.contributor.authorLaleg-Kirati, Taous-Meriemen
dc.contributor.authorGibaru, O.en
dc.date.accessioned2015-08-11T13:44:05Zen
dc.date.available2015-08-11T13:44:05Zen
dc.date.issued2013-02-04en
dc.identifier.isbn9783902823274en
dc.identifier.issn14746670en
dc.identifier.doi10.3182/20130204-3-FR-4032.00208en
dc.identifier.urihttp://hdl.handle.net/10754/565865en
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.en
dc.publisherElsevier BVen
dc.subjectDifferential equationsen
dc.subjectDifferentiatorsen
dc.subjectParameter estimationen
dc.titleFractional order differentiation by integration: An application to fractional linear systemsen
dc.typeConference Paperen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalIFAC Proceedings Volumesen
dc.conference.date4 February 2013 through 6 February 2013en
dc.conference.name6th Workshop on Fractional Differentiation and Its Applications, FDA 2013en
dc.conference.locationGrenobleen
kaust.authorLiu, Dayanen
kaust.authorLaleg-Kirati, Taous-Meriemen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.