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.

The foresight and scenario building methods can be an interesting reference for social sciences, especially in terms of innovative methods for labour process analysis. A scenario – as a central concept for the prospective analysis – can be considered as a rich and detailed portrait of a plausible future world. It can be a useful tool for policy-makers to grasp problems clearly and comprehensively, and to better pinpoint challenges as well as opportunities in an overall framework. The features of the foresight methods are being used in some labour policy making experiences. Case studies developed in Portugal will be presented, and some conclusions will be drawn in order to organise a set of principles for foresight analysis applied to the European project WORKS on the work organisation re-structuring in the knowledge society, and on the work design methods for new management structures of virtual organisations.

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