About this Journal Submit a Manuscript Table of Contents
International Journal of Differential Equations
Volume 2011 (2011), Article ID 304570, 15 pages
http://dx.doi.org/10.1155/2011/304570
Research Article

Existence and Uniqueness Theorem of Fractional Mixed Volterra-Fredholm Integrodifferential Equation with Integral Boundary Conditions

1Department of Mathematics, Faculty of Science, Dohuk University, Kurdistan, Iraq
2Department of Mathematics, Faculty of Science, Zakho University, Kurdistan, Iraq
3Department of Mathematics and Science, College of Education and Basic Sciences, Ajman University of Science and Technology, UAE

Received 7 May 2011; Accepted 24 May 2011

Academic Editor: Shaher Momani

Copyright © 2011 Shayma Adil Murad 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. M. Amairi, M. Aoun, S. Najar, and M. N. Abdelkrim, “A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation,” Applied Mathematics and Computation, vol. 217, no. 5, pp. 2162–2168, 2010. View at Publisher · View at Google Scholar
  2. Z. Drici, F. A. McRae, and J. V. Devi, “Fractional differential equations involving causal operators,” Communications in Applied Analysis., vol. 14, no. 1, pp. 81–88, 2010.
  3. S. B. Hadid, “Local and global existence theorems on differential equations of non-integer order,” Journal of Fractional Calculus, vol. 7, pp. 101–105, 1995. View at Zentralblatt MATH
  4. R. W. Ibrahim, “Existence results for fractional boundary value problem,” International Journal of Contemporary Mathematical Sciences, vol. 3, no. 33-36, pp. 1767–1774, 2008. View at Zentralblatt MATH
  5. S. M. Momani, “Local and global existence theorems on fractional integro-differential equations,” Journal of Fractional Calculus, vol. 18, pp. 81–86, 2000. View at Zentralblatt MATH
  6. S. M. Momani and S. B. Hadid, “On the inequalities of integro-differential fractional equations,” International Journal of Applied Mathematics, vol. 12, no. 1, pp. 29–37, 2003. View at Zentralblatt MATH
  7. B. Ahmad, A. Alsaedi, and B. S. Alghamdi, “Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions,” Nonlinear Analysis Real world Applications, vol. 9, no. 4, pp. 1727–1740, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. H L. Tidke, “Existence of global solutions to nonlinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions,” Electronic Journal of Differential Equations, vol. 2009, pp. No. 55–7, 2009. View at Zentralblatt MATH
  9. B. Ahmad and J. J. Nieto, “Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions,” Boundary Value Problems, vol. 2009, Article ID 708576, 11 pages, 2009. View at Zentralblatt MATH
  10. G. M. N'Guérékata, “A Cauchy problem for some fractional abstract differential equation with non local conditions,” Nonlinear Analysis: Theory , Method and Applications, vol. 70, no. 5, pp. 1873–1876, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. A. Anguraj, P. Karthikeyan, and J. J. Trujillo, “Existence of solutions to fractional mixed integrodifferential equations with nonlocal initial condition,” Advances in Difference Equations, vol. 2011, Article ID 690653, 12 pages, 2011. View at Publisher · View at Google Scholar
  12. 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, Amsterdam, The Netherlands, 2006.
  13. M. A. Krasnosel'skiĭ, “Two remarks on the method of successive approximations,” Uspekhi Matematicheskikh Nauk, vol. 10, no. 1(63), pp. 123–127, 1955.
  14. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
  15. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science, Yverdon, Switzerland, 1993.