On Boundary Value Problems for Fuzzy Differential Equations

  • Rosana Rodríguez-López
Part of the Advances in Soft Computing book series (AINSC, volume 48)

Abstract

In many real phenomena, it is interesting to study the periodic behavior of the magnitudes involved. If a certain natural process is subject to imprecise factors, its modelization can be made by using fuzzy differential equations or fuzzy dynamical systems. The special properties of the functions which are differentiable in the sense of Hukuhara (in particular, the solutions to fuzzy differential equations) make it difficult to handle periodic phenomena by means of fuzzy differential models. We include some considerations on the analysis of boundary value problems associated with fuzzy differential equations from the point of view of Hukuhara-differentiability.

Keywords

Fuzzy differential equations Boundary value problems Periodic solutions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Diamond, P., Kloeden, P.: Metric Spaces of Fuzzy Sets: Theory and Applications. World Scientific Publishing Co., Inc, River Edge (1994)MATHGoogle Scholar
  2. 2.
    Dubois, D., Prade, H.: Fuzzy sets and systems: Theory and applications. Academic Press, New York (1980)MATHGoogle Scholar
  3. 3.
    Kaleva, O.: Fuzzy differential equations. Fuzzy Sets Syst. 24, 301–317 (1987)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kaleva, O.: The Cauchy problem for fuzzy differential equations. Fuzzy Sets Syst. 35, 389–396 (1990)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Lakshmikantham, V., Mohapatra, R.N.: Theory of Fuzzy Differential Equations and Inclusions. Taylor & Francis, London (2003)MATHGoogle Scholar
  6. 6.
    Nieto, J.J., Rodríguez-López, R.: Applications of contractive-like mapping principles to fuzzy and fuzzy differential equations. Rev. Mat. Complut. 19, 361–383 (2006)MATHMathSciNetGoogle Scholar
  7. 7.
    Nieto, J.J., Rodríguez-López, R.: Complete lattices in fuzzy real line (preprint, 2007)Google Scholar
  8. 8.
    Rodríguez-López, R.: Periodic boundary value problems for impulsive fuzzy differential equations. Fuzzy Sets Syst. 159, 1384–1409 (2008)CrossRefGoogle Scholar
  9. 9.
    Rodríguez-López, R.: Comparison results for fuzzy differential equations. Inform. Sci. 178, 1756–1779 (2008)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Rodríguez-López, R.: Monotone method for fuzzy differential equations. Fuzzy Sets Syst. (in press, 2008) doi:10.1016/j.fss.2007.12.020Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Rosana Rodríguez-López
    • 1
  1. 1.Departamento de Análisis Matemático, Facultad de MatemáticasUniversidad de Santiago de CompostelaSantiago de CompostelaSpain

Personalised recommendations