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Linked References

1. 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.
2. N. U. Ahmed, Dynamic Systems and Control with Application, World Scientific, Hackensack, NJ, USA, 2006.
3. 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. View at Scopus
4. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
5. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
6. 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.
7. K. S. Miller and B. Ross, An Introduction to Fractional Calculus and Fractional Differential Equation, Wiley, New York, NY, USA, 1993.
8. I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, Calif, USA, 1999.
9. V. Lakshmikantham, S. Leela, and J. D. Vasundhara, Theory of Fractional Dynamics Systems, Cambridge Scientific, Cambridge, UK, 2009.
10. V. E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, Heidelberg, Germany, 2010. View at Publisher · View at Google Scholar
11. 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. View at Publisher · View at Google Scholar
12. 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.
13. 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.
14. 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. View at Zentralblatt MATH
15. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
16. 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. View at Publisher · View at Google Scholar
17. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
18. 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.
19. 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. View at Publisher · View at Google Scholar
20. 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. View at Publisher · View at Google Scholar
21. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
22. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
23. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
24. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
25. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
26. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
27. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
28. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
29. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
30. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
31. X. Fu, “Controllability of neutral functional differential systems in abstract space,” Applied Mathematics and Computation, vol. 141, no. 2-3, pp. 281–296, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
32. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
33. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
34. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
35. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
36. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
37. M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergano Press, New York, NY, USA, 1964.
38. B. N. Sadovskiĭ, “On a fixed point principle,” Akademija Nauk SSSR, vol. 1, no. 2, pp. 74–76, 1967.
39. 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. View at Publisher · View at Google Scholar
40. J. K. Hale and J. Kato, “Phase space for retarded equations with infinite delay,” Funkcialaj Ekvacioj, vol. 21, no. 1, pp. 11–41, 1978. View at Zentralblatt MATH
41. Y. Hino, S. Murakami, and T. Naito, Functional-differential equations with infinite delay, vol. 1473 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1991.
42. C.-M. Marle, Mesures et Probabilités, Hermann, Paris, France, 1974.