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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 387629, 15 pages
Some Existence Results for Impulsive Nonlinear Fractional Differential Equations with Closed Boundary Conditions
1Department of Mathematics, Faculty of Sciences, Yuzuncu Yil University, 65080 Van, Turkey
2Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Malaysia
Received 30 September 2012; Accepted 22 October 2012
Academic Editor: Beata Rzepka
Copyright © 2012 Hilmi Ergören and Adem Kiliçman. 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.
- K. Diethelm, The Analysis of Fractional Differential Equations, Springer, 2010.
- N. Heymans and I. Podlubny, “Physical interpretation of initial conditions for fractional differential equationswith Riemann Liouville fractional derivatives,” Rheologica Acta, vol. 45, no. 5, pp. 765–772, 2006.
- R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
- 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.
- V. Lakshmikantham, S. Leela, and J. Vasundhara Devi, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, UK, 2009.
- J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Eds., Advances in Fractional Calculus: Theoretical Developmentsand Applications in Physics and Engineering, Springer, Dordrecht, The Netherlands, 2007.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach Science, Yverdon, Switzerland, 1993.
- R. P. Agarwal, M. Benchohra, and S. Hamani, “Boundary value problems for fractional differential equations,” Georgian Mathematical Journal, vol. 16, no. 3, pp. 401–411, 2009.
- R. P. Agarwal, M. Benchohra, and S. Hamani, “A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions,” Acta Applicandae Mathematicae, vol. 109, no. 3, pp. 973–1033, 2010.
- Z. Bai and H. Lü, “Positive solutions for boundary value problem of nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 311, no. 2, pp. 495–505, 2005.
- M. Belmekki, J. J. Nieto, and R. Rodríguez-López, “Existence of periodic solution for a nonlinear fractional differential equation,” Boundary Value Problems, vol. 2009, Article ID 324561, 18 pages, 2009.
- M. Benchohra, S. Hamani, and S. K. Ntouyas, “Boundary value problems for differential equations with fractional order and nonlocal conditions,” Nonlinear Analysis, vol. 71, no. 7-8, pp. 2391–2396, 2009.
- H. A. H. Salem, “On the fractional order -point boundary value problem in reflexive Banach spaces and weak topologies,” Journal of Computational and Applied Mathematics, vol. 224, no. 2, pp. 565–572, 2009.
- W. Zhong and W. Lin, “Nonlocal and multiple-point boundary value problem for fractional differential equations,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1345–1351, 2010.
- V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
- Y. V. Rogovchenko, “Impulsive evolution systems: main results and new trends,” Dynamics of Continuous, Discrete and Impulsive Systems, vol. 3, no. 1, pp. 57–88, 1997.
- A. M. Samoĭlenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
- B. Ahmad and S. Sivasundaram, “Existence of solutions for impulsive integral boundary value problems of fractional order,” Nonlinear Analysis, vol. 4, no. 1, pp. 134–141, 2010.
- M. Benchohra and B. A. Slimani, “Existence and uniqueness of solutions to impulsive fractional differential equations,” Electronic Journal of Differential Equations, vol. 10, pp. 1–11, 2009.
- G. Wang, B. Ahmad, and L. Zhang, “Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1389–1397, 2011.
- T. A. Burton and C. Kirk, “A fixed point theorem of Krasnoselskii-Schaefer type,” Mathematische Nachrichten, vol. 189, pp. 23–31, 1998.
- A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics, Springer, New York, NY, USA, 2003.