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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 142067, 9 pages
The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order
1School of Mathematics and Statistics, Central South University, Changsha, Hunan 410075, China
2Department of Applied Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, China
3College of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, China
Received 3 August 2013; Revised 17 October 2013; Accepted 8 November 2013; Published 28 January 2014
Academic Editor: Stanislaw Migorski
Copyright © 2014 Xianghu Liu 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.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
- I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999.
- A. A. Kilbas, H. M. Srivastava, and J. Juan Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006.
- Z. Liu and X. Li, “Existence and uniqueness of solutions for the nonlinear impulsive fractional differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 6, pp. 1362–1373, 2013.
- X.-B. Shu and Q. Wang, “The existence and uniqueness of mild solutions for fractional differential equations with nonlocal conditions of order 1 < α < 2,” Computers & Mathematics with Applications, vol. 64, no. 6, pp. 2100–2110, 2012.
- J. Dabas and A. Chauhan, “Existence and uniqueness of mild solution for an impulsive neutral fractional integro-differential equation with infinite delay,” Mathematics and Computer Modelling, vol. 57, no. 3-4, pp. 754–763, 2012.
- E. Bazhlekova, Fractional evolution equations in banach spaces [Ph.D. thesis], Eindhoven University of Technology, 2001.
- L. Kexue and P. Jigen, “Fractional abstract cauchy problems,” Integral Equations and Operator Theory, vol. 70, no. 3, pp. 333–361, 2011.
- J. Wang, M. Fečkan, and Y. Zhou, “On the new concept of solutions and existence results for impulsive fractional evolution equations,” Dynamics of Partial Differential Equations, vol. 8, no. 4, pp. 345–361, 2011.
- V. Lakshmikantham, S. Leela, and J. V. Devi, Theory of Fractional Dynamic Systems, Cambridge Academic, Cambridge, UK, 2009.
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, vol. 44 of Applied Mathematical Sciences, 1983.
- J. R. Wang, M. Fečkan, and Y. Zhou, “Relaxed controls for nonlinear fractional impulsive evolution equations,” Journal of Optimization Theory and Applications, vol. 156, no. 1, pp. 13–32, 2013.
- K. Diethelm, The Analysis of Fractional Differential Equations, Springer, Berlin, Germany, 2010.