Araştırma Makalesi
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Second Order Fuzzy Boundary Value Problem with Fuzzy Parameter

Yıl 2020, Cilt: 10 Sayı: 1, 584 - 594, 01.03.2020
https://doi.org/10.21597/jist.572407

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.

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.

Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi

Yıl 2020, Cilt: 10 Sayı: 1, 584 - 594, 01.03.2020
https://doi.org/10.21597/jist.572407

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.

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.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Matematik
Bölüm Matematik / Mathematics
Yazarlar

Nihat Altınışık Bu kişi benim 0000-0002-3187-2800

Tahir Ceylan 0000-0002-8914-4240

Yayımlanma Tarihi 1 Mart 2020
Gönderilme Tarihi 31 Mayıs 2019
Kabul Tarihi 14 Kasım 2019
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 1

Kaynak Göster

APA Altınışık, N., & Ceylan, T. (2020). Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi. Journal of the Institute of Science and Technology, 10(1), 584-594. https://doi.org/10.21597/jist.572407
AMA Altınışık N, Ceylan T. Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi. Iğdır Üniv. Fen Bil Enst. Der. Mart 2020;10(1):584-594. doi:10.21597/jist.572407
Chicago Altınışık, Nihat, ve Tahir Ceylan. “Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi”. Journal of the Institute of Science and Technology 10, sy. 1 (Mart 2020): 584-94. https://doi.org/10.21597/jist.572407.
EndNote Altınışık N, Ceylan T (01 Mart 2020) Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi. Journal of the Institute of Science and Technology 10 1 584–594.
IEEE N. Altınışık ve T. Ceylan, “Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi”, Iğdır Üniv. Fen Bil Enst. Der., c. 10, sy. 1, ss. 584–594, 2020, doi: 10.21597/jist.572407.
ISNAD Altınışık, Nihat - Ceylan, Tahir. “Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi”. Journal of the Institute of Science and Technology 10/1 (Mart 2020), 584-594. https://doi.org/10.21597/jist.572407.
JAMA Altınışık N, Ceylan T. Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi. Iğdır Üniv. Fen Bil Enst. Der. 2020;10:584–594.
MLA Altınışık, Nihat ve Tahir Ceylan. “Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi”. Journal of the Institute of Science and Technology, c. 10, sy. 1, 2020, ss. 584-9, doi:10.21597/jist.572407.
Vancouver Altınışık N, Ceylan T. Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi. Iğdır Üniv. Fen Bil Enst. Der. 2020;10(1):584-9.