Generalized Grünwald–Letnikov Fractional Derivative and Its Laplace and Fourier Transforms

Manuel Duarte Ortigueira

doi:10.1115/1.4003136

Generalized Grünwald–Letnikov Fractional Derivative and Its Laplace and Fourier Transforms

Manuel Duarte Ortigueira

DEE2010-B2 Sistemas

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

24 Citations (Scopus)

Abstract

The generalized Grünwald–Letnikov fractional derivative is analyzed in this paper. Its Laplace and Fourier transforms are computed, and some current results are criticized. It is shown that only the forward derivative of a sinusoid exists. This result is used to define the frequency response of a fractional linear system.

Original language	Unknown
Pages (from-to)	034501
Journal	Journal Of Computational And Nonlinear Dynamics
Volume	6
Issue number	3
DOIs	https://doi.org/10.1115/1.4003136
Publication status	Published - 1 Jan 2011

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10.1115/1.4003136

http://oa.uninova.pt/4747/

Cite this

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abstract = "The generalized Gr{\"u}nwald–Letnikov fractional derivative is analyzed in this paper. Its Laplace and Fourier transforms are computed, and some current results are criticized. It is shown that only the forward derivative of a sinusoid exists. This result is used to define the frequency response of a fractional linear system.",

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AB - The generalized Grünwald–Letnikov fractional derivative is analyzed in this paper. Its Laplace and Fourier transforms are computed, and some current results are criticized. It is shown that only the forward derivative of a sinusoid exists. This result is used to define the frequency response of a fractional linear system.

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