Research Article

On the Graphical Analysis of a Fuzzy Problem

Volume: 14 Number: 4 December 15, 2024
EN TR

On the Graphical Analysis of a Fuzzy Problem

Abstract

The fuzzy Laplace transform method is very useful to solve fuzzy differential equations and this method is an important method in practice. This paper is on a second-order fuzzy problem. In this study, we research the fuzzy problem with negative fuzzy coefficient using the method of fuzzy Laplace transform. Since we use generalized Hukuhara differentiability, solutions are investigated under the four different situations. A numerical example is given. Graphics of the solutions are drawn for alpha level sets. Conclusions are presented at the end of the paper.

Keywords

Second-order fuzzy problem , fuzzy number , generalized Hukuhara differentiability

References

  1. Akın Ö., Khaniyev T., Bayeğ S. and Türkşen B. (2016). Solving a second order fuzzy initial value problem using the heaviside function, Turkish Journal of Mathematics and Computer Science, 4, 16–25.
  2. Allahviranloo T., Ahmady N. and Ahmady E. (2007). Numerical solution of fuzzy differential equations by predictor-corrector method, Information Sciences, 177(7), 1633-1647.
  3. Allahviranloo T. and Ahmadi M. B. (2010). Fuzzy Laplace transforms, Soft Computing, 14(3), 235–243.
  4. Allahviranloo T. and Gholami S. (2012). Note on ‘‘Generalized Hukuhara differentiability of interval-valued functions and interval differential equations’’, Journal of Fuzzy Set Valued Analysis, 2012, 1-4.
  5. Bayeğ S., Mert R., Akın Ö. and Khaniyev T. (2022). On a type-2 fuzzy approach to solution of second-order initial value problem, Soft Computing, 26, 1671-1683.
  6. Bede B., Rudas I. J. and Bencsik A. L. (2007). First order linear fuzzy differential equations under generalized differentiability, Information Sciences, 177(7), 1648–1662.
  7. Belhallaj Z., Melliani S., Elomari M. and Chadli L. S. (2023). Application of the intuitionistic fuzzy Laplace transform method for resolution of one dimensional wave equations, International Journal of Difference Equations, 18(1), 211-225.
  8. Eljaoui E. and Melliani S. (2023). A study of some properties of fuzzy Laplace transform with their applications in solving the second-order fuzzy linear partial differential equations, Advances in Fuzzy Systems, 2023(7868762), 1-15.
  9. Gültekin Çitil H. (2019). Comparisons of the exact and the approximate solutions of second-order fuzzy linear boundary value problems, Miskolc Mathematical Notes, 20(2) 823–837.
  10. Gültekin Çitil H. (2020). Solving the fuzzy initial value problem with negative coefficient by using fuzzy Laplace transform, Facta Universitatis, Series: Mathematics and Informatics, 35(1), 201-215.
APA
Gültekin Çitil, H. (2024). On the Graphical Analysis of a Fuzzy Problem. Karadeniz Fen Bilimleri Dergisi, 14(4), 2328-2337. https://doi.org/10.31466/kfbd.1561335