Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.22/4313
Título: Fractional derivatives: probability interpretation and frequency response of rational approximations
Autor: Machado, J. A. Tenreiro
Palavras-chave: Fractional derivative
Fractional calculus
Probabilistic interpretation
Frequency response
Fraction approximations
Data: 2009
Editora: Elsevier
Relatório da Série N.º: Communications in Nonlinear Science and Numerical Simulation; Vol. 14, Issues 9-10
Resumo: The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.
Peer review: yes
URI: http://hdl.handle.net/10400.22/4313
ISSN: 1007-5704
Versão do Editor: http://www.sciencedirect.com/science/article/pii/S1007570409000859
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