- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
International Journal of Differential Equations
Volume 2011 (2011), Article ID 304570, 15 pages
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.
- 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.
- 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.
- 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.
- 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.
- S. M. Momani, “Local and global existence theorems on fractional integro-differential equations,” Journal of Fractional Calculus, vol. 18, pp. 81–86, 2000.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- M. A. Krasnosel'skiĭ, “Two remarks on the method of successive approximations,” Uspekhi Matematicheskikh Nauk, vol. 10, no. 1(63), pp. 123–127, 1955.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science, Yverdon, Switzerland, 1993.