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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 818703, 11 pages
http://dx.doi.org/10.1155/2012/818703
Research Article

A Note on Fractional Differential Equations with Fractional Separated Boundary Conditions

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Received 21 January 2012; Accepted 8 February 2012

Academic Editor: Shaher Momani

Copyright © 2012 Bashir Ahmad and Sotiris K. Ntouyas. 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. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. View at Zentralblatt MATH
  2. G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford, UK, 2008. View at Zentralblatt MATH
  3. 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 Science B.V., Amsterdam, The Netherlands, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. R. L. Magin, Fractional Calculus in Bioengineering, Begell House Publisher, West Redding, Conn, USA, 2006.
  5. J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Eds., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, The Netherlands, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. R. P. Agarwal, M. Belmekki, and M. Benchohra, “A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative,” Advances in Difference Equations, Article ID 981728, p. 47, 2009. View at Zentralblatt MATH
  7. B. Ahmad and S. Sivasundaram, “Existence and uniqueness results for nonlinear boundary value problems of fractional differential equations with separated boundary conditions,” Communications in Applied Analysis, vol. 13, no. 1, pp. 121–127, 2009. View at Zentralblatt MATH
  8. B. Ahmad and J. J. Nieto, “Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions,” Computers & Mathematics with Applications, vol. 58, no. 9, pp. 1838–1843, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. B. Ahmad, “Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations,” Applied Mathematics Letters, vol. 23, no. 4, pp. 390–394, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. B. Ahmad and J. J. Nieto, “Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory,” Topological Methods in Nonlinear Analysis, vol. 35, no. 2, pp. 295–304, 2010.
  11. D. Baleanu, O. G. Mustafa, and R. P. Agarwal, “An existence result for a superlinear fractional differential equation,” Applied Mathematics Letters, vol. 23, no. 9, pp. 1129–1132, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. E. Hernandez, D. O'Regan, and K. Balachandran, “On recent developments in the theory of abstract differential equations with fractional derivatives,” Nonlinear Analysis, vol. 73, no. 10, pp. 3462–3471, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. B. Ahmad and S. Sivasundaram, “On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order,” Applied Mathematics and Computation, vol. 217, no. 2, pp. 480–487, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. B. Ahmad, S. K. Ntouyas, and A. Alsaedi, “New existence results for nonlinear fractional differential equations with three-point integral boundary conditions,” Advances in Difference Equations, Article ID 107384, p. 11, 2011. View at Zentralblatt MATH
  15. B. Ahmad and S. K. Ntouyas, “A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order,” Electronic Journal of Qualitative Theory of Differential Equations, no. 22, p. 15, 2011.
  16. B. Ahmad and R. P. Agarwal, “On nonlocal fractional boundary value problems,” Dynamics of Continuous, Discrete & Impulsive Systems Series A, vol. 18, no. 4, pp. 535–544, 2011. View at Zentralblatt MATH
  17. M. A. Krasnoselskii, “Two remarks on the method of successive approximations,” Uspekhi Matematicheskikh Nauk, vol. 10, pp. 123–127, 1955.
  18. A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics, Springer, New York, NY, USA, 2005.