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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 871912, 24 pages
http://dx.doi.org/10.1155/2012/871912
Research Article

Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics

1Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
2Faculty of Computer Science, Białystok University of Technology, 15-351 Białystok, Poland

Received 1 January 2012; Revised 25 February 2012; Accepted 27 February 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Tatiana Odzijewicz et al. 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 study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free-boundary value problems. The fractional action-like variational approach (FALVA) is extended and some applications to physics discussed.