Research Grants 23/06478-1 - Cálculo fracionário, Lógica fuzzy - BV FAPESP
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Fractional variational calculus, Herglotz variational principle, and apllications.

Abstract

This project aims to develop basic research in fractional calculus and variational calculus with applications in physics. Calculus with derivatives and integrals of non-integer order began more than three centuries ago when Leibniz proposed a derivative of order 1/2. Despite being almost as old as the usual calculus, only in the last three decades has fractional calculus begun to gain more attention due to the emergence of applications in various areas of physics and engineering. Onthe other hand, the variational calculus, through the principle of least action, isone of the fundamental pillars of physics. Generalizations of the principle of leastaction for Lagrangians dependent on fractional derivatives proved to be important tools for the analysis of several physical systems. In this work we propose to develop and analyze extensions and generalizations of the variational calculus behind the inclusion of fractional derivatives, and through the variational principle of Herglotz. (AU)

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