On the Usefulness of Riemann-Liouville and Caputo Derivatives in Describing Fractional Shift-invariant Linear Systems

Fernando José Almeida Vieira do Coito; Manuel Duarte Ortigueira; DEE Group Author

On the Usefulness of Riemann-Liouville and Caputo Derivatives in Describing Fractional Shift-invariant Linear Systems

Fernando José Almeida Vieira do Coito, Manuel Duarte Ortigueira, DEE Group Author

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

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 condi- tions may be either null or unavailable. This may lead to question the use of such derivatives.

Original language	Unknown
Pages (from-to)	113-124
Journal	Journal of Computational and Nonlinear Dynamics
Volume	1
Issue number	2
Publication status	Published - 1 Jan 2012

Cite this

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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 condi- tions may be either null or unavailable. This may lead to question the use of such derivatives.",

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

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AU - Ortigueira, Manuel Duarte

AU - DEE Group Author

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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 condi- tions 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 condi- tions may be either null or unavailable. This may lead to question the use of such derivatives.

KW - Initial value problem

KW - Fractional derivative

KW - Fractional linear system

M3 - Article

SN - 1555-1415

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SP - 113

EP - 124

JO - Journal of Computational and Nonlinear Dynamics

JF - Journal of Computational and Nonlinear Dynamics

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