Fractional Calculus: D'où venons-nous? Que sommes-nous? Où allons-nous?

Abstract

© 2016 Diogenes Co., Sofia. Discussions under this title, inspired by the famous Gauguin painting, were held during a Round Table in frames of the International Conference "Fractional Differentiation and Applications" (ICFDA '16) held in Novi Sad (Serbia), 18-20 July 2016, http://www.icfda16.com/public/; see details at Announcements (21 September Closure): http://icfda16.com/public/announcements.php; and Report on ICFDA '16 in Editorial Note in this journal's issue, pp. 1059-1060. Along with the presentations made during this Round Table, we include here some contributions by the participants sent afterwards and also by few colleagues planning but failed to attend. The intention of these discussions was to continue the useful traditions from the first conferences on Fractional Calculus (FC) topics, to pose open problems, challenging hypotheses and questions "where to go", "how to save and improve the prestige of FC", to share opinions and try to find ways to resolve them.