A coherent approach to non-integer order derivatives
- Citation:
- Ortigueira, M. 2006. A coherent approach to non-integer order derivatives. Signal Processing. 86:2505–2515., Number 10: Elsevier
Abstract:
The relation showing that the Grunwald-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 regularised version that makes the concept of pseudo-function appear naturally without the need for a rejection of any infinite part. From the regularised derivative, new formulations are deduced and specialised first for the real functions and afterwards for functions with Laplace transforms obtaining the definitions proposed by Lionville. With these tools suitable definitions of fractional linear systems are obtained.
Notes:
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