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Abstract and Applied Analysis
Volume 2012, Article ID 890396, 15 pages
http://dx.doi.org/10.1155/2012/890396
Research Article

On Riesz-Caputo Formulation for Sequential Fractional Variational Principles

1Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Çankaya University, 06530 Ankara, Turkey
2Institute for Space Sciences, P.O. Box MG-23, 76900 Magurele-Bucharest, Romania

Received 6 October 2011; Accepted 23 December 2011

Academic Editor: Wing-Sum Cheung

Copyright © 2012 Fahd Jarad 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.

Linked References

  1. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, Elsevier Science, Amsterdam, The Netherlands, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Linghorne, Pa, USA, 1993, Theory and Applications. View at Zentralblatt MATH
  3. R. L. Magin, Fractional Calculus in Bioengineering, Begell House, Redding, Conn, USA, 2006.
  4. N. Heymans and I. Podlubny, “Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives,” Rheologica Acta, vol. 45, pp. 765–771, 2006. View at Google Scholar
  5. I. S. Jesus and J. A. Tenreiro Machado, “Fractional control of heat diffusion systems,” Nonlinear Dynamics, vol. 54, no. 3, pp. 263–282, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. F. Mainardi, Y. Luchko, and G. Pagnini, “The fundamental solution of the space-time fractional diffusion equation,” Fractional Calculus & Applied Analysis, vol. 4, no. 2, pp. 153–192, 2001. View at Google Scholar · View at Zentralblatt MATH
  7. E. Scalas, R. Gorenflo, and F. Mainardi, “Uncoupled continuous-time random walks: solution and limiting behavior of the master equation,” Physical Review E, vol. 69, no. 1, artice 011107, 2004. View at Publisher · View at Google Scholar
  8. O. P. Agrawal and D. Baleanu, “A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems,” Journal of Vibration and Control, vol. 13, no. 9-10, pp. 1269–1281, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. V. E. Tarasov and G. M. Zaslavsky, “Nonholonomic constraints with fractional derivatives,” Journal of Physics A, vol. 39, no. 31, pp. 9797–9815, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. Y. Chen, “Fractional calculus, delay dynamics and networked control systems,” in Proceedings of the 3rd International Symposium on Resilient Control Systems (ISRCS '10), pp. 58–63, Idaho Falls, Idhao, USA, August 2010.
  11. S. Bhalekar, V. Daftardar-Gejji, D. Baleanu, and R. Magin, “Fractional Bloch equation with delay,” Computers & Mathematics with Applications, vol. 61, no. 5, pp. 1355–1365, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. J. F. Rosenblueth, “Systems with time delay in the calculus of variations: a variational approach,” Journal of Mathematical Control and Information, vol. 5, no. 2, pp. 125–145, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. T. Abdeljawad, F. Jarad, and D. Baleanu, “Variational optimal-control problems with delayed arguments on time scales,” Advances in Difference Equations, vol. 2009, Article ID 840386, 15 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. D. K. Hughes, “Variational and optimal control problems with delayed argument,” Journal of Optimization Theory and Applications, vol. 2, no. 1, pp. 1–15, 1968. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. O. P. Agrawal, “A general formulation and solution scheme for fractional optimal control problems,” Nonlinear Dynamics, vol. 38, no. 1–4, pp. 323–337, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. D. Baleanu, T. Maaraba, and F. Jarad, “Fractional variational principles with delay,” Journal of Physics. A, vol. 41, no. 31, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. F. Jarad, T. Abdeljawad, and D. Baleanu, “Fractional variational principles with delay within Caputo derivatives,” Reports on Mathematical Physics, vol. 65, no. 1, pp. 17–28, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, Calif, USA, 1999. View at Zentralblatt MATH
  19. O. P. Agrawal, “Fractional variational calculus in terms of Riesz fractional derivatives,” Journal of Physics, vol. 40, no. 24, pp. 6287–6303, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. B. van Brunt, The Calculus of Variations, Springer, New York, NY, USA, 2004.