Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi

Bu makalede iki nokta sınır değer problemi genelleştirilmiş Hukuhara türevi (gh-türev) ile incelenmiştir. Bu yöntemin dört farklı çözümü vardır. Bu çözümler ayrı ayrı incelenerek elde edilen sonuçlar sunulmuştur. Yöntemin uygulanabilirliği bir örnekle gösterilmiştir.

Second Order Fuzzy Boundary Value Problem with Fuzzy Parameter

In this article two point fuzzy boundary value problem is examined under the approach generalized Hukuhara differentiability (gH-differentiability). There are four different solutions for the problem by using a generalized differentiability. These solutions are analyzed separately and the results are presented. The method's applicability is illustrated with an example.

___

  • Armand A, Gouyandeh Z, 2013. Solving two-point fuzzy boundary problem using iteration method. Communications on Advanced Computational Science with Applications, 1-10.
  • Bede B, Gal SG, 2005. Generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equation. Fuzzy Sets and Systems, 151: 581–599.
  • Bede B, Stefanini L, 2012. Generalized differentiability of fuzzy-valued functions. Fuzzy Sets and Systems. 230: 119-141.
  • Diamond P, Kloeden P, 1994. Metric Spaces of Fuzzy Sets: Theory and Applications. World Scientific, Singapore.
  • Dubois D, Prade H, 1980. Fuzzy Sets and Systems. Theory and Aplications, Academic Press, New York.
  • Goetschel J, Voxman W, 1986. Elementary fuzzy calculus. Fuzzy Sets and Systems, 18(1): 31-43.
  • Gomes LT, Barros LC, Bede B, 2010. Fuzzy Differential Equations in Various Approaches. pp.120, London.
  • Gültekin H, Altınışık N, 2014. On boundary value problems for second-order fuzzy linear differential equations with constant coefficients. Journal of Advances in Mathematics, 8(3): 1614-1631.
  • Gültekin H, Altınışık N, 2014. On solution of two-point fuzzy boundary value problems. Bulletin of Society for Mathematical Services & Standarts, 11: 31-39.
  • Gültekin Çitil H, 2018. Comparison results of linear differential equations with fuzzy boundary values. Journal of Science and Arts, 1(42): 33-48.
  • Hukuhara M, 1967. Integration des applications mesurables dont la valeur est un compact convex. Funkcialaj Ekvacioj, 10: 205–229.
  • Kaleva O, 1987. Fuzzy differetial equations. Fuzzy Sets and Systems, 24: 301-317.
  • Kaleva O, Seikkala S, 1984. On fuzzy metric spaces. Fuzzy Sets and Systems, 12: 215-229.
  • Khastan A, Nieto JJ, 2010. A boundary value problem for second order differential equations. Nonlinear Analysis, 72: 43-54.
  • Klir GJ, Yuan B, 1995. Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall PTR, Upper Saddle River, New Jersey.
  • MATLAB, 2016. Fuzzy Logic Toolbox Version. R2016a.
  • Nasseri H, 2008. Fuzzy Numbers: Positive and Nonnegative. International Mathematical Forum, 3: 1777-1780.
  • Puri. M, Ralescu D, 1983. Differential and fuzzy functions. Journal of Mathematical Analysis and Applications, 91: 552–558.
  • Zadeh LA, 1965. Fuzzy sets. Information and Control, 8(3): 338–353.
Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi-Cover
  • ISSN: 2146-0574
  • Yayın Aralığı: Yılda 4 Sayı
  • Başlangıç: 2011
  • Yayıncı: -