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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.

Citations to this Article [10 citations]

The following is the list of published articles that have cited the current article.

  • Matheus J. Lazo, and Delfim F. M. Torres, “The DuBois–Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler–Lagrange Equation Involving Only Derivatives of Caputo,” Journal of Optimization Theory and Applications, vol. 156, no. 1, pp. 56–67, 2012. View at Publisher · View at Google Scholar
  • A. B. Malinowska, and D. F. M. Torres, “Fractional calculus of variations of several independent variables,” European Physical Journal-Special Topics, vol. 222, no. 8, pp. 1813–1826, 2013. View at Publisher · View at Google Scholar
  • Rami Ahmad El-Nabulsi, “Non-standard fractional Lagrangians,” Nonlinear Dynamics, 2013. View at Publisher · View at Google Scholar
  • A. R. El-Nabulsi, “Modified Proca equation and modified dispersion relation from a power-law Lagrangian functional,” Indian Journal Of Physics, vol. 87, no. 5, pp. 465–470, 2013. View at Publisher · View at Google Scholar
  • Dongling Wang, and Aiguo Xiao, “Numerical Methods for Fractional Variational Problems Depending on Indefinite Integrals,” Journal of Computational and Nonlinear Dynamics, vol. 8, no. 2, 2013. View at Publisher · View at Google Scholar
  • Tatiana Odzijewicz, Agnieszka B. Malinowska, and Delfim F. M. Torres, “Green's theorem for generalized fractional derivatives,” Fractional Calculus and Applied Analysis, vol. 16, no. 1, pp. 64–75, 2013. View at Publisher · View at Google Scholar
  • Loïc Bourdin, “Existence of a weak solution for fractional Euler–Lagrange equations,” Journal of Mathematical Analysis and Applications, vol. 399, no. 1, pp. 239–251, 2013. View at Publisher · View at Google Scholar
  • Shakoor Pooseh, Ricardo Almeida, and Delfim F.M. Torres, “Discrete direct methods in the fractional calculus of variations,” Computers & Mathematics with Applications, 2013. View at Publisher · View at Google Scholar
  • Giorgio S. Taverna, and Delfim F.M. Torres, “Generalized fractional operators for nonstandard Lagrangians,” Mathematical Methods in the Applied Sciences, 2014. View at Publisher · View at Google Scholar
  • Loic Bourdin, Tatiana Odzijewicz, and Delfim F. M. Torres, “Existence Of Minimizers For Generalized Lagrangian Functionals And A Necessary Optimality Condition - Application To Fractional Variational Problems,” Differential and Integral Equations, vol. 27, no. 7-8, pp. 743–766, 2014. View at Publisher · View at Google Scholar