Technical Briefs

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

[+] Author and Article Information
Manuel D. Ortigueira

 UNINOVA/DEE, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Campus da FCT da UNL, Quinta da Torre, 2825-114 Monte da Caparica, Portugalmdo@fct.unl.pt

Juan J. Trujillo

Departamento de Análisis Matemático, University La Laguna, La Laguna, 38271 Tenerife, Spainjtrujill@ullmat.es

We will return to this subject later.

J. Comput. Nonlinear Dynam 6(3), 034501 (Mar 02, 2011) (3 pages) doi:10.1115/1.4003136 History: Received January 04, 2010; Revised November 12, 2010; Published March 02, 2011; Online March 02, 2011

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.

Copyright © 2011 by American Society of Mechanical Engineers
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