Table of Contents
Conference Papers in Mathematics
Volume 2013, Article ID 872869, 5 pages
http://dx.doi.org/10.1155/2013/872869
Conference Paper

Fractional Variational Problems Depending on Fractional Derivatives of Differentiable Functions with Application to Nonlinear Chaotic Systems

Instituto de Matemática, Estatística e Física, Universidade Federal do Rio Grande, 96.201-900 Rio Grande, RS, Brazil

Received 15 June 2013; Accepted 14 July 2013

Academic Editors: G. S. F. Frederico, N. Martins, D. F. M. Torres, and A. J. Zaslavski

This Conference Paper is based on a presentation given by Matheus Jatkoske Lazo at “The Cape Verde International Days on Mathematics 2013” held from 22 April 2013 to 25 April 2013 in Praia, Cape Verde.

Copyright © 2013 Matheus Jatkoske Lazo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We formulate a necessary condition for functionals with Lagrangians depending on fractional derivatives of differentiable functions to possess an extremum. The Euler-Lagrange equation we obtained generalizes previously known results in the literature and enables us to construct simple Lagrangians for nonlinear systems. As examples of application, we obtain Lagrangians for some chaotic dynamical systems.