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International Journal of Differential Equations
Volume 2013 (2013), Article ID 191060, 12 pages
An Alternative Method for the Study of Impulsive Differential Equations of Fractional Orders in a Banach Space
Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria
Received 15 April 2013; Accepted 14 July 2013
Academic Editor: Fawang Liu
Copyright © 2013 Asma Bouzaroura and Saïd Mazouzi. 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.
- W. M. Ahmad and R. El-Khazali, “Fractional-order dynamical models of love,” Chaos, Solitons and Fractals, vol. 33, no. 4, pp. 1367–1375, 2007.
- B. Bonilla, M. Rivero, L. Rodríguez-Germá, and J. J. Trujillo, “Fractional differential equations as alternative models to nonlinear differential equations,” Applied Mathematics and Computation, vol. 187, no. 1, pp. 79–88, 2007.
- K. Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics, Springer, Berlin, Germany, 2010.
- E. Hernández, D. O'Regan, and K. Balachandran, “On recent developments in the theory of abstract differential equations with fractional derivatives,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 73, no. 10, pp. 3462–3471, 2010.
- V. Lakshmikantham, “Theory of fractional functional differential equations,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 69, no. 10, pp. 3337–3343, 2008.
- V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
- V. Lakshmikantham, S. Leela, and D. J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Scientific, Cambridge, UK, 2009.
- V. E. Tarasov, Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, Heidelberg, Germany, 2011.
- M. Benchohra and B. A. Slimani, “Existence and uniqueness of solutions to impulsive fractional differential equations,” Electronic Journal of Differential Equations, vol. 2009, article 10, 11 pages, 2009.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
- I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science, Longhorne, Pa, USA, 1993.
- K. Balachandran, S. Kiruthika, and J. J. Trujillo, “Remark on the existence results for fractional impulsive integrodifferential equations in Banach spaces,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 6, pp. 2244–2247, 2012.
- K. Balachandran, S. Kiruthika, and J. J. Trujillo, “Existence results for fractional impulsive integrodifferential equations in Banach spaces,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 1970–1977, 2011.
- O. K. Jaradat, A. Al-Omari, and S. Momani, “Existence of the mild solution for fractional semilinear initial value problems,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 69, no. 9, pp. 3153–3159, 2008.
- G. M. Mophou and G. M. N'Guérékata, “Existence of the mild solution for some fractional differential equations with nonlocal conditions,” Semigroup Forum, vol. 79, no. 2, pp. 315–322, 2009.
- G. M. N'Guérékata, “A Cauchy problem for some fractional abstract differential equation with non local conditions,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 70, no. 5, pp. 1873–1876, 2009.
- M. Fečkan, Y. Zhou, and J. Wang, “On the concept and existence of solution for impulsive fractional differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 7, pp. 3050–3060, 2012.
- L. Mahto, S. Abbas, and A. Favini, “Analysis of Caputo impulsive fractional order differential equations,” International Journal of Differential Equations, vol. 2013, Article ID 704547, 11 pages, 2013.
- B. Nagy and F. Riesz, Functional Analysis, Blackie & Son, London, UK, 1956.
- W. Wei, X. Xiang, and Y. Peng, “Nonlinear impulsive integro-differential equations of mixed type and optimal controls,” Optimization, vol. 55, no. 1-2, pp. 141–156, 2006.