DOI QR코드

DOI QR Code

Existence of Periodic Solutions for Fuzzy Differential Equations

  • Received : 2010.05.21
  • Accepted : 2010.09.07
  • Published : 2010.09.30

Abstract

In this paper, we investigate the existence and calculation of the expression of periodic solutions for fuzzy differential equations with three types of forcing terms, by using Hukuhara derivative. In particular, Theorems 3.2, 4.2 and 5.2 are the results of existences of periodic solutions for fuzzy differential equations I, II and III, respectively. These results will help us to study phenomena with periodic peculiarity such as wave or sound.

Keywords

References

  1. J.C. Chang, H. Chen, S.M. Shyu and W.C. Lian, “Fixed-pint theorems in fuzzy realline,” Comput. Math. Appl., vol.47, pp. 845-851, 2004. https://doi.org/10.1016/S0898-1221(04)90068-5
  2. P. Diamond and P.E. Kloeden, Metric Spaces of Fuzzy Sets, World Scientific, Singapore, 1994.
  3. Y.C. Kwun, M.J. Kim, J.S. Park and J.H. Park, “Continuously initial observability for the semilinear fuzzy integrodifferential equations,” Proceedings in 6th International Conference on Fuzzy Systems and Knowledge Discovery, vol. 1, pp.225-229, 2008. https://doi.org/10.1109/FSKD.2008.510
  4. Y.C. Kwun, J.S. Kim, M.J. Park and J.H. Park, “Non-local controllability for the semilinear fuzzy integrodifferential equations in n-dimensional fuzzy vector space,” Advances in Difference Equations, vol. 2009, Article ID734090, 2009. https://doi.org/10.1155/2009/734090
  5. J.Y. Park, Y.C. Kwun and J.M. Jeong, “Existence of periodic solutions for delay evolution integrodifferential equations,” Math. Comp. Model., vol. 40, pp.597-603, 2004. https://doi.org/10.1016/j.mcm.2003.09.040
  6. J.Y. Park, I.H. Jung and M.J. Lee, “Almost periodic solutions of fuzzy systems,” Fuzzy Sets Syst., vol. 119, pp. 367-373, 2001. https://doi.org/10.1016/S0165-0114(98)00439-4
  7. M. Puri and D. Ralescu, “Differential and fuzzy functions,” J. Math. Anal. Appl., vol. 91, pp. 552-558, 1983. https://doi.org/10.1016/0022-247X(83)90169-5
  8. J.J. Nieto and R.R. Lopez, “Existence of extremal solutions for quadratic fuzzy equations,” Fixed Point Theory Appl., vol. 3, pp. 321-342, 2005. https://doi.org/10.1155/FPTA.2005.321
  9. J.J. Nieto, R.R. Lopez and D.Franco, “Linear first-order fuzzy differential equations,” Fuzziness and Know., vol. 6, 687-709, 2006.
  10. A. Pazy, Semigroups of linear operators and applications of partial differential equations, Springer-Verlag, New York, 1983.
  11. J.H. Liu, “Bounded and periodic solutions of finite delay evolution equations,” Non. Anal. vol. 34, pp. 101-111, 1998. https://doi.org/10.1016/S0362-546X(97)00606-8
  12. R.R. Lopez, “Monotone method for fuzzy differential equations,” Fuzzy Sets Syst., vol. 159, 2047-2076, 2008. https://doi.org/10.1016/j.fss.2007.12.020
  13. R.R. Lopez, “Periodic boundary value problems for impulsive fuzzy differential equations,” Fuzzy Sets Syst., vol. 159, 1384-1409, 2008. https://doi.org/10.1016/j.fss.2007.09.005
  14. B. Bede and S.G. Gal, “Almost periodic fuzzy-number-valued functions,” Fuzzy Sets Syst., vol. 147, pp. 385-403, 2004. https://doi.org/10.1016/j.fss.2003.08.004
  15. V. Lakshmikantham and R.N. Mohapatra, Theory of Fuzzy Differential Equations and Inclusions, Taylor and Francis, London, 2004.

Cited by

  1. Exact Controllability for Fuzzy Differential Equations in Credibility Space vol.14, pp.2, 2014, https://doi.org/10.5391/IJFIS.2014.14.2.145