Second Order Fuzzy Boundary Value Problem with Fuzzy Parameter

Yıl 2020, Cilt: 10 Sayı: 1, 584 - 594, 01.03.2020

Nihat Altınışık Tahir Ceylan

https://doi.org/10.21597/jist.572407

https://izlik.org/JA68AB22MN

Öz

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.

Anahtar Kelimeler

Generalized Hukuhara differentiability , fuzzy boundary value problem , generalized solution

Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi

https://izlik.org/JA68AB22MN

Öz

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.

Anahtar Kelimeler

Genelleştirilmiş Hukuhara türevi , bulanık sınır değer problemi , genelleştirilmiş çözüm

Kaynakça

• 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.