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Fractional centred differences and derivatives definitions are proposed generalising to real orders the existing ones valid for even and odd positive integer orders. For each one, suitable integral formulations are obtained. The computations of the involved integrals lead to new generalisations of the Cauchy integral derivative. To compute this integral, a… (More)

The relation showing that the Gru¨nwald-Letnikov and generalised Cauchy derivatives are equal is presented. This establishes a bridge between two different formulations and simultaneously between the classic integer order derivatives and the fractional ones. Starting from the generalised Cauchy derivative formula, new relations are obtained, namely a… (More)

The initial condition problem for fractional linear system initialisation is studied in this paper. It is based on the generalised initial value theorem. The new approach involves functions belonging to the space of Laplace transformable distributions verifying the Watson–Doetsch lemma. The fractional derivatives of these functions are independent of the… (More)

A look into Fractional Calculus and their applications from the Signal Processing point of view is done in this paper. A coherent approach to the fractional derivative is presented leading to notions that are, not only compatible with the classic, but constitute a true generalization. This means that the classic are recovered when the fractional domain is… (More)

In this paper a new least-squares (LS) approach is used to model the discrete-time fractional differintegrator. This approach is based on a mismatch error between the required response and the one obtained by the difference equation defining the auto-regressive, moving-average (ARMA) model. In minimizing the error power we obtain a set of suitable normal… (More)