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Journal of Vibration and Control
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Fractional Central Differences and Derivatives

Manuel Duarte Ortigueira

UNINOVA and Department of Electrical Engineering, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Campus da FCT da UNL, Quinta da Torre, 2825 114 Monte da Caparica, Portugal, mdo{at}fct.unl.pt

Fractional central differences and derivatives are studied in this article. These are generalisations to real orders of the ordinary positive (even and odd) integer order differences and derivatives, and also coincide with the well known Riesz potentials. The coherence of these definitions is studied by applying the definitions to functions with Fourier transformable functions. Some properties of these derivatives are presented and particular cases studied.

Key Words: Fractional central difference • fractional central derivative • Grünwald-Letnikov • generalized Cauchy derivative

Journal of Vibration and Control, Vol. 14, No. 9-10, 1255-1266 (2008)
DOI: 10.1177/1077546307087453
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