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Journal of Applied Mathematics
Volume 2012, Article ID 916543, 19 pages
http://dx.doi.org/10.1155/2012/916543
Research Article

On Nonlinear Neutral Fractional Integrodifferential Inclusions with Infinite Delay

1School of Mathematics, Yunnan Normal University, Kunming 650092, China
2Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
3Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan

Received 12 February 2012; Accepted 25 February 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Fang Li 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.

Linked References

  1. 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, Article ID 981728, 47 pages, 2009. View at Google Scholar
  2. M. Caputo, Elasticit`a e Dissipazione, Zanichelli, Bologna, Italy, 1969.
  3. 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.
  4. F. Li, “Solvability of nonautonomous fractional integrodifferential equations with infinite delay,” Advances in Difference Equations, Article ID 806729, 18 pages, 2011. View at Google Scholar
  5. K. Balachandran and J. J. Trujillo, “The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces,” Nonlinear Analysis, Theory, Methods and Applications, vol. 72, no. 12, pp. 4587–4593, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. Z.-W. Lv, J. Liang, and T.-J. Xiao, “Solutions to fractional differential equations with nonlocal initial condition in Banach spaces,” Advances in Difference Equations, Article ID 340349, 10 pages, 2010. View at Google Scholar
  7. F. Mainardi, P. Paradisi, and R. Gorenflo, “Probability distributions generated by fractional diffusion equations,” in Econophysics: An Emerging Science, J. Kertesz and I. Kondor, Eds., Kluwer, Dordrecht, The Netherlands, 2000. View at Google Scholar
  8. G. M. Mophou and G. M. N'Guérékata, “Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay,” Applied Mathematics and Computation, vol. 216, no. 1, pp. 61–69, 2010. View at Publisher · View at Google Scholar
  9. I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, Calif, USA, 1999.
  10. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach Science Publishers, Yverdon, Switzerland, 1993.
  11. R.-N. Wang, D.-H. Chen, and T.-J. Xiao, “Abstract fractional Cauchy problems with almost sectorial operators,” Journal of Differential Equations, vol. 252, no. 1, pp. 202–235, 2012. View at Publisher · View at Google Scholar
  12. J. Henderson and A. Ouahab, “Fractional functional differential inclusions with finite delay,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 5, pp. 2091–2105, 2009. View at Publisher · View at Google Scholar
  13. V. Obukhovski and P. Zecca, “Controllability for systems governed by semilinear differential inclusions in a Banach space with a noncompact semigroup,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 9, pp. 3424–3436, 2009. View at Publisher · View at Google Scholar
  14. J. Liang and T.-J. Xiao, “The Cauchy problem for nonlinear abstract functional differential equations with infinite delay,” Computers & Mathematics with Applications, vol. 40, no. 6-7, pp. 693–703, 2000. View at Publisher · View at Google Scholar
  15. J. Liang and T.-J. Xiao, “Solvability of the Cauchy problem for infinite delay equations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 58, no. 3-4, pp. 271–297, 2004. View at Publisher · View at Google Scholar
  16. J. Liang and T.-J. Xiao, “Solutions to nonautonomous abstract functional equations with infinite delay,” Taiwanese Journal of Mathematics, vol. 10, no. 1, pp. 163–172, 2006. View at Google Scholar
  17. J. Liang, T. J. Xiao, and F. L. Huang, “Solvability and stability of abstract functional-differential equations with unbounded delay,” Sichuan Daxue Xuebao, vol. 31, no. 1, pp. 8–14, 1994. View at Google Scholar
  18. J. Liang, T.-J. Xiao, and J. van Casteren, “A note on semilinear abstract functional differential and integrodifferential equations with infinite delay,” Applied Mathematics Letters, vol. 17, no. 4, pp. 473–477, 2004. View at Publisher · View at Google Scholar
  19. J. H. Liu, “Periodic solutions of infinite delay evolution equations,” Journal of Mathematical Analysis and Applications, vol. 247, no. 2, pp. 627–644, 2000. View at Publisher · View at Google Scholar
  20. T.-J. Xiao and J. Liang, “Blow-up and global existence of solutions to integral equations with infinite delay in Banach spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 12, pp. e1442–e1447, 2009. View at Publisher · View at Google Scholar
  21. T.-J. Xiao, X.-X. Zhu, and J. Liang, “Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 11, pp. 4079–4085, 2009. View at Publisher · View at Google Scholar
  22. K. Deimling, Multivalued Differential Equations, Walter de Gruyter, Berlin, Germany, 1992.
  23. M. Martelli, “A Rothe's type theorem for non-compact acyclic-valued maps,” Bollettino della Unione Matematica Italiana, vol. 11, supplement, no. 3, pp. 70–76, 1975. View at Google Scholar
  24. A. Lasota and Z. Opial, “An application of the Kakutani—Ky Fan theorem in the theory of ordinary differential equations,” Bulletin de l'Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 13, pp. 781–786, 1965. View at Google Scholar
  25. D. Henry, Geometric Theory of Semilinear Parabolic Partial Differential Equations, Springer, Berlin, Germany, 1989.
  26. T.-J. Xiao and J. Liang, The Cauchy Problem for Higher-order Abstract Differential Equations, vol. 1701 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1998.