On the fractional central differences and derivatives

• Author(s): Ortigueira, M.D.
• Date: 2008
• Persistent ID: http://hdl.handle.net/10362/1718
• Origin: Repositório Institucional da UNL
• Subject(s): Fractional central difference; fractional central derivative; Grünwald-Letnikov; generalized Cauchy derivative
• Document Type: Article
• Language: English

Description

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.