About this Journal Submit a Manuscript Table of Contents
Advances in Mathematical Physics
Volume 2013 (2013), Article ID 426061, 5 pages
http://dx.doi.org/10.1155/2013/426061
Research Article

Existence of Solutions for Fractional Differential Inclusions with Separated Boundary Conditions in Banach Space

1Department of Mathematics, Laboratory of Dynamical Systems and Control, Larbi Ben M'hidi University, P.O. Box 358, Oum El Bouaghi, Algeria
2Department of Mathematics, Guelma University, 24000 Guelma, Algeria
3Department of Mathematics and Computer Sciences, Cankaya University, 06530 Ankara, Turkey
4Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
5Institute of Space Sciences, Magurele-Bucharest, Romania

Received 10 March 2013; Accepted 11 May 2013

Academic Editor: Changpin Li

Copyright © 2013 Mabrouk Bragdi 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. R. P. Agarwal, D. O'Regan, and S. Staněk, “Positive solutions for mixed problems of singular fractional differential equations,” Mathematische Nachrichten, vol. 285, no. 1, pp. 27–41, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B. Ahmad, J. J. Nieto, and J. Pimentel, “Some boundary value problems of fractional differential equations and inclusions,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1238–1250, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. B. Ahmad and S. K. Ntouyas, “A note on fractional differential equations with fractional separated boundary conditions,” Abstract and Applied Analysis, vol. 2012, Article ID 818703, 11 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Z. Bai and W. Sun, “Existence and multiplicity of positive solutions for singular fractional boundary value problems,” Computers & Mathematics with Applications, vol. 63, no. 9, pp. 1369–1381, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. Caballero, J. Harjani, and K. Sadarangani, “Positive solutions for a class of singular fractional boundary value problems,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1325–1332, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. I. J. Cabrera, J. Harjani, and K. B. Sadarangani, “Existence and uniqueness of positive solutions for a singular fractional three-point boundary value problem,” Abstract and Applied Analysis, vol. 2012, Article ID 803417, 18 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Jin, X. Liu, and M. Jia, “Existence of positive solutions for singular fractional differential equations with integral boundary conditions,” Electronic Journal of Differential Equations, vol. 2012, no. 63, pp. 1–14, 2012. View at MathSciNet
  8. D. O'Regan and S. Stanek, “Fractional boundary value problems with singularities in space variables,” Nonlinear Dynamics, vol. 71, no. 4, pp. 641–652, 2013. View at Publisher · View at Google Scholar
  9. B. Ahmad and S. K. Ntouyas, “Boundary value problems for n-th order differential inclusions with four-point integral boundary conditions,” Opuscula Mathematica, vol. 32, no. 2, pp. 205–226, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  10. A. Boucherif and N. Al-Malki, “Solvability of Neumann boundary-value problems with Carathéodory nonlinearities,” Electronic Journal of Differential Equations, vol. 2004, no. 51, pp. 1–7, 2004. View at Zentralblatt MATH · View at MathSciNet
  11. G. A. Chechkin, D. Cioranescu, A. Damlamian, and A. L. Piatnitski, “On boundary value problem with singular inhomogeneity concentrated on the boundary,” Journal de Mathématiques Pures et Appliquées, vol. 98, no. 2, pp. 115–138, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. A. Nouy, M. Chevreuil, and E. Safatly, “Fictitious domain method and separated representations for the solution of boundary value problems on uncertain parameterized domains,” Computer Methods in Applied Mechanics and Engineering, vol. 200, no. 45-46, pp. 3066–3082, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. M. Bragdi and M. Hazi, “Existence and uniqueness of solutions of fractional quasilinear mixed integrodifferential equations with nonlocal condition in Banach spaces,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 2012, no. 51, pp. 1–16, 2012. View at MathSciNet
  14. A. Debbouche and D. Baleanu, “Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1442–1450, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. A. Debbouche and D. Baleanu, “Exact null controllability for fractional nonlocal integrodifferential equations via implicit evolution system,” Journal of Applied Mathematics, vol. 2012, Article ID 931975, 17 pages, 2012. View at Publisher · View at Google Scholar
  16. A. Debbouche, D. Baleanu, and R. P. Agarwal, “Nonlocal nonlinear integrodifferential equations of fractional orders,” Boundary Value Problems, vol. 2012, article 78, pp. 1–10, 2012. View at Publisher · View at Google Scholar
  17. C. Kou, H. Zhou, and C. Li, “Existence and continuation theorems of Riemann-Liouville type fractional differential equations,” International Journal of Bifurcation and Chaos, vol. 22, no. 4, Article ID 1250077, 12 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. C. Li and Y. Ma, “Fractional dynamical system and its linearization theorem,” Nonlinear Dynamics, vol. 71, no. 4, pp. 621–633, 2013.
  19. C. P. Li and F. R. Zhang, “A survey on the stability of fractional differential equations,” The European Physical Journal: Special Topics, vol. 193, no. 1, pp. 27–47, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier, Amsterdam, The Netherlands, 2006.
  21. I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1993.
  22. T. M. Atanackovic and B. Stankovic, “Generalized wave equation in nonlocal elasticity,” Acta Mechanica, vol. 208, no. 1-2, pp. 1–10, 2009. View at Publisher · View at Google Scholar · View at Scopus
  23. M. Caputo, “Linear models of dissipation whose q is almost frequency independent—part II,” Geophysical Journal of the Royal Astronomical Society, vol. 13, pp. 529–539, 1967.
  24. D. Delbosco and L. Rodino, “Existence and uniqueness for a nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 204, no. 2, pp. 609–625, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. T. Qiu and Z. Bai, “Existence of positive solutions for singular fractional differential equations,” Electronic Journal of Differential Equations, vol. 2008, no. 146, pp. 1–9, 2008. View at Zentralblatt MATH · View at MathSciNet
  26. M. Aitaliobrahim, “Neumann boundary-value problems for differential inclusions in banach spaces,” Electronic Journal of Differential Equations, vol. 2010, no. 104, pp. 1–5, 2010. View at Scopus