TY - GEN

T1 - Fractional order differentiation by integration: An application to fractional linear systems

AU - Liu, Dayan

AU - Laleg-Kirati, Taous-Meriem

AU - Gibaru, O.

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2013/2/24

Y1 - 2013/2/24

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/565865

UR - https://linkinghub.elsevier.com/retrieve/pii/S147466701534893X

UR - http://www.scopus.com/inward/record.url?scp=84881083991&partnerID=8YFLogxK

U2 - 10.3182/20130204-3-FR-4032.00208

DO - 10.3182/20130204-3-FR-4032.00208

M3 - Conference contribution

SN - 9783902823274

SP - 653

EP - 658

BT - IFAC Proceedings Volumes

PB - Elsevier BV

ER -