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International Journal of Differential Equations
Volume 2012, Article ID 521750, 38 pages
http://dx.doi.org/10.1155/2012/521750
Review Article

Generalized Multiparameters Fractional Variational Calculus

Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, IL 62901, USA

Received 2 April 2012; Accepted 8 August 2012

Academic Editor: Fawang Liu

Copyright © 2012 Om Prakash Agrawal. 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 [9 citations]

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

  • Tomasz Nartowicz, Ewa Pawluszewicz, and Arkadiusz Mystkowski, “Robust fractional order controller for a linear active magnetic bearing system,” 2017 22nd International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 658–663, . View at Publisher · View at Google Scholar
  • Om P. Agrawal, “Survey paper : Some generalized fractional calculus operators and their applications in integral equations,” Fractional Calculus and Applied Analysis, vol. 15, no. 4, pp. 700–711, 2012. View at Publisher · View at Google Scholar
  • Yufeng Xu, and Om P. Agrawal, “Numerical solutions and analysis of diffusion for new generalized fractional advection-diffusion equations,” Central European Journal of Physics, vol. 11, no. 10, pp. 1178–1193, 2013. View at Publisher · View at Google Scholar
  • Rajesh K. Pandey, and Om P. Agrawal, “Numerical scheme for generalized isoperimetric constraint variational problems with a-operator,” Proceedings of the ASME Design Engineering Technical Conference, vol. 4, 2013. View at Publisher · View at Google Scholar
  • Vasily E. Tarasov, and Elias C. Aifantis, “Non-Standard Extensions of Gradient Elasticity: Fractional Non- Locality, Memory and Fractality,” Communications in Nonlinear Science and Numerical Simulation, 2014. View at Publisher · View at Google Scholar
  • Yufeng Xu, Zhimin He, and Qinwu Xu, “Numerical solutions of fractional advection-diffusion equations with a kind of new generalized fractional derivative,” International Journal of Computer Mathematics, vol. 91, no. 3, pp. 588–600, 2014. View at Publisher · View at Google Scholar
  • Vasily E. Tarasov, “Variational principle of stationary action for fractional nonlocal media and fields,” Pacific Journal of Mathematics for Industry, vol. 7, no. 1, 2015. View at Publisher · View at Google Scholar
  • Om P. Agrawal, and Yufeng Xu, “Generalized vector calculus on convex domain,” Communications In Nonlinear Science And Numerical Simulation, vol. 23, no. 1-3, pp. 129–140, 2015. View at Publisher · View at Google Scholar
  • Rajesh K. Pandey, and Om P. Agrawal, “Numerical Scheme for a Quadratic Type Generalized Isoperimetric Constraint Variational Problems With A-Operator,” Journal Of Computational And Nonlinear Dynamics, vol. 10, no. 2, 2015. View at Publisher · View at Google Scholar