Dept. of Electrical Engineering
Polytechnic of Porto, Portugal
J. A. Tenreiro Machado was born at 1957. He graduated with ‘Licenciatura’ (1980), PhD. (1989) and ‘Habilitation’ (1995), in Electrical and Computer Engineering at the University of Porto. During 1980-1998 he worked at the Dept. of Electrical and Computer Engineering of the University of Porto. Since 1998 he works at the Institute of Engineering, Polytechnic Institute of Porto. He is presently Principal Coordinator Professor at the Dept. of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Portugal. He published 108 chapters of international books, 420 papers in international journals, 369 papers in international conferences, 4 books in Portuguese, 6 books in English. He has a Scopus h-index=49, and non-self-citations: 10859 to September 2019.
His research interests include: Complex systems, Nonlinear Dynamics, Fractional Calculus, Modelling, Entropy, Control, Data series analysis, Biomathematics, Evolutionary Computing, Genomics, and Robotics and Mechatronics.
Talk: Fractional calculus: Emerging applications
Fractional Calculus (FC) started with the standard differential calculus but remained an obscure topic during almost three centuries. The present-day popularity of FC in the scientific arena, with a growing number of researchers and published papers, makes one forget that 20 years ago the topic was considered “exotic” and that a typical question was “FC, what is it useful for?”
We recall two remarkable foreseeing quotes about FC: “It will lead to a paradox, from which one day useful consequences will be drawn” (G. Leibniz, 1695) and “The fractional calculus is the calculus of the XXI century” (K. Nishimoto, 1991). Indeed, new advanced and emerging areas of application of the future of FC.
Present day popular directions of progress are the formulation of new operators, the “fractionalization” of integer models, the further development of known topics and the pursuit for new areas of application. The first two, namely the proposal for new definitions of fractional-order operators, or the fractionalization of some mathematical models, may represent critical adventures with possible misleading or even erroneous formulations. The third, that is, the in-depth study of some mathematical and computational fields, constitute a solid option, but its lack of ambition narrows considerably the scope of FC. The fourth option leads to exploring new applications, both with mathematical and computational tools, and represents a challenging strategy for the progress of FC.
Possible new directions of progress in FC may emerge in the fringe of classical science, or in the borders between two or more distinct areas. The lecture presents some uncommon ideas and topics, namely the application of computational and visualization methods for the analysis of data series and the characterization of complex phenomena.