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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 529025, 11 pages
Complete Controllability of Fractional Neutral Differential Systems in Abstract Space
1School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan Province 410076, China
2School of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi Province 530006, China
3Changsha University of Science and Technology, Changsha, Hunan, China
Received 10 September 2012; Revised 9 November 2012; Accepted 10 November 2012
Academic Editor: Yong Zhou
Copyright © 2013 Fang Wang 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. Diethelm and A. D. Freed, “On the solution of nonlinear fractional order differential equations used in the modeling of viscoelasticity,” in Scientific Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties, F. Keil, W. Machens, H. Voss, and J. Werther, Eds., pp. 217–224, Springer, Heidelberg, Germany, 1999.
- N. U. Ahmed, Dynamic Systems and Control with Application, World Scientific, Hackensack, NJ, USA, 2006.
- Y. A. Rossikhin and M. V. Shitikova, “Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids,” Applied Mechanics Reviews, vol. 50, no. 1, pp. 15–67, 1997.
- L. Debnath, “Recent applications of fractional calculus to science and engineering,” International Journal of Mathematics and Mathematical Sciences, vol. 2003, no. 54, pp. 3413–3442, 2003.
- 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, Amsterdam, The Netherland, 2006.
- K. S. Miller and B. Ross, An Introduction to Fractional Calculus and Fractional Differential Equation, Wiley, New York, NY, USA, 1993.
- I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, Calif, USA, 1999.
- V. Lakshmikantham, S. Leela, and J. D. Vasundhara, Theory of Fractional Dynamics Systems, Cambridge Scientific, Cambridge, UK, 2009.
- V. E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, Heidelberg, Germany, 2010.
- F. Wang, “Existence and uniqueness of solutions for a nonlinear fractional differential equation,” Journal of Applied Mathematics and Computing, vol. 39, no. 1-2, pp. 53–67, 2012.
- F. Wang, Z. H. Liu, and P. Wang, “Analysis of a system for linear fractional equaitons,” Journal of Applied Mathematics, vol. 2012, Article ID 193061, 21 pages, 2012.
- F. Wang and Z. H. Liu, “Anti-periodic fractional boundary value problems for nonlinear differential equations of fractional order,” Advances in Difference Equation, vol. 2012, artilce 116, 12 pages, 2012.
- R. P. Agarwal, M. Belmekki, and M. Benchohra, “A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative,” Advances in Difference Equations, vol. 2009, Article ID 981728, 47 pages, 2009.
- M. M. El-Borai, “Some probability densities and fundamental solutions of fractional evolution equations,” Chaos, Solitons and Fractals, vol. 14, no. 3, pp. 433–440, 2002.
- Y. Zhou and F. Jiao, “Nonlocal Cauchy problem for fractional evolution equations,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 4465–4475, 2010.
- K. Balachandran and R. Sakthivel, “Controllability of functional semilinear integrodifferential systems in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 255, no. 2, pp. 447–457, 2001.
- K. Balachanadran and E. R. Anandhi, “Controllability of neurtal functional integrodifferential infinite delay systems in Banach spaces,” Nonlinear Analysis, vol. 61, pp. 405–423, 2005.
- J. R. Wang and Y. Zhou, “Complete controllability of fractional evolution systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 11, pp. 4346–4355, 2012.
- J. R. Wang, Z. Fan, and Y. Zhou, “Nonlocal controllability of semilinear dynamic systems with fractional derivative in Banach spaces,” Journal of Optimization Theory and Applications, vol. 154, no. 1, pp. 292–302, 2012.
- J. Wang and Y. Zhou, “A class of fractional evolution equations and optimal controls,” Nonlinear Analysis: Real World Applications, vol. 12, no. 1, pp. 262–272, 2011.
- J. Wang, Y. Zhou, and W. Wei, “A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 10, pp. 4049–4059, 2011.
- J. Wang and Y. Zhou, “Analysis of nonlinear fractional control systems in Banach spaces,” Nonlinear Analysis: Theory, Methods and Applications A, vol. 74, no. 17, pp. 5929–5942, 2011.
- R. Sakthivel, N. I. Mahmudov, and Juan. J. Nieto, “Controllability for a class of fractional-order neutral evolution control systems,” Applied Mathematics and Computation, vol. 218, no. 20, pp. 10334–10340, 2012.
- Y. Ren, L. Hu, and R. Sakthivel, “Controllability of impulsive neutral stochastic functional differential inclusions with infinite delay,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2603–2614, 2011.
- R. Sakthivel, Y. Ren, and N. I. Mahmudov, “On the approximate controllability of semilinear fractional differential systems,” Computers and Mathematics with Applications, vol. 62, no. 3, pp. 1451–1459, 2011.
- K. Rykaczewski, “Approximate controllability of differential inclusions in Hilbert spaces,” Nonlinear Analysis: Theory, Methods and Applications A, vol. 75, no. 5, pp. 2701–2712, 2012.
- R. Sakthivel, S. Suganya, and S. M. Anthoni, “Approximate controllability of fractional stochastic evolution equations,” Computers and Mathematics with Applications, vol. 63, no. 3, pp. 660–668, 2012.
- R. Sakthivel and Y. Ren, “Complete controllability of stochastic evolution equations with jumps,” Reports on Mathematical Physics, vol. 68, no. 2, pp. 163–174, 2011.
- Y.-K. Chang and D. N. Chalishajar, “Controllability of mixed Volterra-Fredholm-type integro-differential inclusions in Banach spaces,” Journal of the Franklin Institute, vol. 345, no. 5, pp. 499–507, 2008.
- X. Fu, “Controllability of neutral functional differential systems in abstract space,” Applied Mathematics and Computation, vol. 141, no. 2-3, pp. 281–296, 2003.
- S. Ji, G. Li, and M. Wang, “Controllability of impulsive differential systems with nonlocal conditions,” Applied Mathematics and Computation, vol. 217, no. 16, pp. 6981–6989, 2011.
- Z. Tai, “Controllability of fractional impulsive neutral integrodifferential systems with a nonlocal Cauchy condition in Banach spaces,” Applied Mathematics Letters, vol. 24, no. 12, pp. 2158–2161, 2011.
- E. Hernández M. and D. O'Regan, “Controllability of Volterra-Fredholm type systems in Banach spaces,” Journal of the Franklin Institute, vol. 346, no. 2, pp. 95–101, 2009.
- 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 and Applications A, vol. 73, no. 10, pp. 3462–3471, 2010.
- Y. Zhou and F. Jiao, “Existence of mild solutions for fractional neutral evolution equations,” Computers and Mathematics with Applications, vol. 59, no. 3, pp. 1063–1077, 2010.
- M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergano Press, New York, NY, USA, 1964.
- B. N. Sadovskiĭ, “On a fixed point principle,” Akademija Nauk SSSR, vol. 1, no. 2, pp. 74–76, 1967.
- P. Zhao and J. Zheng, “Remarks on Hausdorff measure and stability for the p-obstacle problem,” Proceedings Mathematical Sciences, vol. 122, no. 1, pp. 129–137, 2012.
- J. K. Hale and J. Kato, “Phase space for retarded equations with infinite delay,” Funkcialaj Ekvacioj, vol. 21, no. 1, pp. 11–41, 1978.
- Y. Hino, S. Murakami, and T. Naito, Functional-differential equations with infinite delay, vol. 1473 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1991.
- C.-M. Marle, Mesures et Probabilités, Hermann, Paris, France, 1974.