Advances in Difference Equations
Volume 2011 (2011), Article ID 357580, 9 pages
Fractional-Order Variational Calculus with Generalized Boundary Conditions
1Faculty of Science, Zagazig University, Zagazig, Egypt
2Faculty of Science in Zulfi, Majmaah University, Zulfi 11932, P.O. Box 1712, Saudi Arabia
3Department of Mathematics and Computer Science, Çankaya University, 06530 Ankara, Turkey
4Institute for Space Sciences, P.O.Box MG-23 Magurele, 76900 Bucharest, Romania
Received 18 September 2010; Accepted 8 November 2010
Academic Editor: J. J. Trujillo
Copyright © 2011 Mohamed A. E. Herzallah and Dumitru Baleanu. 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.
This paper presents the necessary and sufficient optimality conditions for fractional variational problems involving the right and the
left fractional integrals and fractional derivatives defined in the sense
of Riemman-Liouville with a Lagrangian depending on the free end-points. To illustrate our approach, two examples are discussed in detail.