Initialized in France in 1975, the school of thought on fractional differentiation in automatic control has reached for some years a good level of scientific maturation attested by the interest and the quality of research carried out in this domain as well as its impact on the industrial world. 

Beyond an important scientific production which can be measured by the number of publications, thesis, patents and distinctions, efforts of research animation in this domain are also significant, judging in the number of events organized: session, working group meetings or summer school. 

Regarding the federation of research in this domain, it is materialized by a project of the "GDR Automatique" involving five laboratories and entitled "Fractional differentiation in vibration insulation".  Given the end of such a project, as well as the maturity degree reached by our community in this domain, it has appeared us appropriate to revive the federative action which was initialized in 1996 with about fifteen French laboratories which has, at various degrees, a measurable activity on fractional differentiation and its applications. 

The working group "Fractional systems and their applications" is an idea resulting of such a reflection. It was launched under the aegis of the Club EEA, of the SEE, of the GDR SDSE and Automatic of the CNRS and of the French Ministry of Research, with the support of industrial groups, notably the PSA and ALSTOM societies
 

Moreover, given that the automobile sector and notably the vehicle dynamics is an application field par excellence for the automaticians, it seems to us appropriate to orient applications toward the automobile sector. This choice, consisting in the application of fractional differentiation to this privileged sector, is supported by the INRETS and the GDR CHMAC. Such a choice should permit to ensure the applications consistency of fractional differentiation in this domain and to encourage the integration of such an operator in the various thematic aspects that this domain overlap. 

The working group results from a focusing of the "Automatic control and Applications" working group on a specific thematic, namely "the fractional systems". 
 
The theoretical aspects will be reinforced by an overture to the applied math community, its immersion in the automatic control community being certainly nature to encourage answers to automatician problematics. 

Application aspects will be reinforced by an overture to the industrial world. Support of the SEE must encourage the involvement of industrial. The presentation, by the authors (industrial and academic), of the most successful technological transfers according to the socioeconomic sector demand, will be a factor in favor of the development of an applicable/applied research. 

While borrowing to the "Automatic control and Teaching" working group launched by "the Club EEA", the educational aspects will be concretized by the didactic presentation aiming to facilitate the educational introduction of research results in teachings of level BAC + 5 or possibly BAC + 4. The underlying idea is indeed to help our colleagues to develop teaching of fractional differentiation with educational supports for course and TD. As un example, such an experience is conducted with CRONE control. 

Moreover, the shared culture of the various EEA disciplinary would encourage in the concerned domain, exchanges between electricians, electrotechnicans and automaticians, and would contribute to the  EEA unit recess  in a scientific environment defined by the SEE and the various CNRS research group. 

In a period where the methodological approaches in the field of fractional systems display a satisfactory progression, we have also to see the emergence of mathematical approaches in signal, systems and control theory, which could enrich the fractional systems theory at the concepts level and also in the resulting formalism. Such approaches can be based on the conception of new tools or on the existing tool extensions which was not the subject of advanced developments. So that they reinforce the theoretical corpus of our disciplines and escape to a dilution in the vast mathematical sector, they must be validated or valorized by specific applications which highlight their interest facing the industrial problematic of our disciplines. 

Given that the CRONE team has carried out sustained research activities since 1975 in the fractional system thematic, it will contribute naturally to the scientific politic definition of the working group, notably through a federative, animation and attraction part of the industrial community.   

The action we have launched is motivated by the concern to identify, to unify and thus to increase the consistency of the studies and applications of  fractional differentiation. Thus our intention is to realize the following objectives and actions :
 

•  to affirm in France and in the world a fundamental, methodological and applied research initialized in France in the 1970's;  

• to reinforce the advance of  the French community in this type of research

• to collect colleagues of " free electron" type having displayed, to various degree, a particular interest in the thematic of the working group while starting a personal research which must be taken into account; 

• to encourage relations with the European and International Community which don't stop to increase and which obviously want to make contact with us;  

• to reorient this kind of research in order to make it more pertinent; to this effect, the scientific animation of the working group should permit to avoid: classics traps resulting of the absence of dialogue and of coordination which lead to discover known results, to fall in well known deadlock, to solve problems without theoretical or application interest;  

• to encourage the validation and the valorization of the theoretical research results, not only in the EEA domain but also in all the domains the engineering sciences or in biologic and physico-chemical sciences. These validations and valorizations could be industrial applications but also software developments or test bench realizations;
  

Given that the automobile sector and more precisely the vehicle dynamics is an application field par excellence for the automatician, it appeared us appropriate to orient applications toward the car industry. Note that the choice consisting in the application of fractional differentiation to this privileged sector is sponsored by the INRETS and the GDR CHMAC. Such a choice should permit to ensure the consistency of fractional differentiation applications in this domain and should permit to encourage the integration of such an operator in the various thematic aspects of this domain.