Research Article
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Second Order Fuzzy Boundary Value Problem with Fuzzy Parameter

Year 2020, , 584 - 594, 01.03.2020

Nihat Altınışık Tahir Ceylan

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

Abstract

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.

Keywords

Generalized Hukuhara differentiability fuzzy boundary value problem generalized solution

References

  • 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

Year 2020, , 584 - 594, 01.03.2020

Nihat Altınışık Tahir Ceylan

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

Abstract

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.

Keywords

Genelleştirilmiş Hukuhara türevi bulanık sınır değer problemi genelleştirilmiş çözüm

References

  • 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.
There are 19 citations in total.

Details

Primary Language Turkish
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Nihat Altınışık This is me 0000-0002-3187-2800

Tahir Ceylan 0000-0002-8914-4240

Publication Date March 1, 2020
Submission Date May 31, 2019
Acceptance Date November 14, 2019
Published in Issue Year 2020

Cite

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. J. Inst. Sci. and Tech. March 2020;10(1):584-594. doi:10.21597/jist.572407
Chicago Altınışık, Nihat, and Tahir Ceylan. “Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi”. Journal of the Institute of Science and Technology 10, no. 1 (March 2020): 584-94. https://doi.org/10.21597/jist.572407.
EndNote Altınışık N, Ceylan T (March 1, 2020) Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi. Journal of the Institute of Science and Technology 10 1 584–594.
IEEE N. Altınışık and T. Ceylan, “Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi”, J. Inst. Sci. and Tech., vol. 10, no. 1, pp. 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 (March 2020), 584-594. https://doi.org/10.21597/jist.572407.
JAMA Altınışık N, Ceylan T. Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi. J. Inst. Sci. and Tech. 2020;10:584–594.
MLA Altınışık, Nihat and Tahir Ceylan. “Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi”. Journal of the Institute of Science and Technology, vol. 10, no. 1, 2020, pp. 584-9, doi:10.21597/jist.572407.
Vancouver Altınışık N, Ceylan T. Bulanık Parametreli İkinci Mertebeden Bulanık Sınır Değer Problemi. J. Inst. Sci. and Tech. 2020;10(1):584-9.