Generalised fractional centred differences and derivatives are studied in this chapter. Keywords Fractional centred difference, fractional centred derivative, Grünwald–Letnikov derivative, generalised Cauchy derivative.
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Ortigueira, MD, (2005) Fractional Differences Integral Representation and its Use to Define Fractional Derivatives, In: Proceedings of the ENOC-2005, Fifth EUROMECH Nonlinear Dynamics Conference, Eindhoven University of Technology, The Netherlands, August, 7-12.
Ortigueira MD, Coito F (2004) From Differences to Differintegrations, Fract. Calc. Appl. Anal. 7(4).
Ortigueira MD (2006) A coherent approach to non integer order derivatives, Signal Processing, special issue on Fractional Calculus and Applications.
Diaz IB, Osler TI (1974) Differences of fractional order, Math. Comput. 28 (125).
Ortigueira MD (2006) Fractional Centred Differences and Derivatives, to be presented at the IFAC FDA Workshop to be held at Porto, Portugal, 19-21 July, 2006.
Ortigueira MD (2005) Riesz potentials via centred derivatives submitted for publication in the Int. J. Math. Math. Sci. December 2005.
Okikiolu GO (1966) Fourier Transforms of the operator Hα, Proceedings of Cambridge Philosophy Society 62, 73-78.
Andrews GE, Askey R, Roy R (1999) Special Functions, Cambridge University Press, Cambridge.
Henrici P (1974) Applied and Computational Complex Analysis, Vol. 1. Wiley, pp. 270-271.
Samko SG, Kilbas AA, Marichev OI (1987) Fractional Integrals and Derivatives - Theory and Applications. Gordon and Breach Science, New York.
Ortigueira MD (2000) Introduction to Fractional Signal Processing. Part 2: Discrete-Time Systems, In: IEE Proceedings on Vision, Image and Signal Processing, No.1, February 2000, pp. 71-78.
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Ortigueira, M.D. (2007). Riesz Potentials as Centred Derivatives. In: Sabatier, J., Agrawal, O.P., Machado, J.A.T. (eds) Advances in Fractional Calculus. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6042-7_7
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