On the usefulness of Riemann-Liouville and Caputo derivatives in describing fractional shift-invariant linear systems

Manuel D. Ortigueira; Fernando J. Coito

doi:10.5890/JAND.2012.05.001

On the usefulness of Riemann-Liouville and Caputo derivatives in describing fractional shift-invariant linear systems

Manuel D. Ortigueira, Fernando J. Coito

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

The description of shift-invariant systems in terms of Riemann- Liouville and Caputo derivatives is studied according to their "initial conditions". The situation of a past excitation of a linear system is considered and shown that the referred initial conditions may be either null or unavailable. This may lead to question the use of such derivatives.

Original language	English
Pages (from-to)	113-124
Number of pages	12
Journal	Journal of Applied Nonlinear Dynamics
Volume	1
Issue number	2
DOIs	https://doi.org/10.5890/JAND.2012.05.001
Publication status	Published - 2012

Keywords

Fractional derivative
Fractional linear system
Initial value problem

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10.5890/JAND.2012.05.001

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title = "On the usefulness of Riemann-Liouville and Caputo derivatives in describing fractional shift-invariant linear systems",

abstract = "The description of shift-invariant systems in terms of Riemann- Liouville and Caputo derivatives is studied according to their {"}initial conditions{"}. The situation of a past excitation of a linear system is considered and shown that the referred initial conditions may be either null or unavailable. This may lead to question the use of such derivatives.",

keywords = "Fractional derivative, Fractional linear system, Initial value problem",

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note = "Publisher Copyright: {\textcopyright} 2012 L \& H Scientific Publishing, LLC.",

year = "2012",

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T1 - On the usefulness of Riemann-Liouville and Caputo derivatives in describing fractional shift-invariant linear systems

AU - Ortigueira, Manuel D.

AU - Coito, Fernando J.

PY - 2012

Y1 - 2012

N2 - The description of shift-invariant systems in terms of Riemann- Liouville and Caputo derivatives is studied according to their "initial conditions". The situation of a past excitation of a linear system is considered and shown that the referred initial conditions may be either null or unavailable. This may lead to question the use of such derivatives.

AB - The description of shift-invariant systems in terms of Riemann- Liouville and Caputo derivatives is studied according to their "initial conditions". The situation of a past excitation of a linear system is considered and shown that the referred initial conditions may be either null or unavailable. This may lead to question the use of such derivatives.

KW - Fractional derivative

KW - Fractional linear system

KW - Initial value problem

UR - https://www.scopus.com/pages/publications/84979630551

U2 - 10.5890/JAND.2012.05.001

DO - 10.5890/JAND.2012.05.001

M3 - Article

AN - SCOPUS:84979630551

SN - 2164-6457

VL - 1

SP - 113

EP - 124

JO - Journal of Applied Nonlinear Dynamics

JF - Journal of Applied Nonlinear Dynamics

IS - 2

ER -

On the usefulness of Riemann-Liouville and Caputo derivatives in describing fractional shift-invariant linear systems

Abstract

Keywords

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