Araştırma Makalesi
BibTex RIS Kaynak Göster

TWO POINT FUZZY BOUNDARY VALUE PROBLEM WITH EXTENSION PRINCIPLE USING HEAVISIDE FUNCTION

Yıl 2023, Cilt: 6 Sayı: 2, 131 - 141, 31.07.2023
https://doi.org/10.33773/jum.1307156

Öz

In this paper we deal with the fuzzy eigenfunctions of the two point fuzzy
boundary value problem (FBVP) with fuzzy coefficient of the boundary
conditions. The fuzzy solution is obtained from the Zadeh's extension
principle using the Heaviside function. The eigenvalues and the fuzzy
eigenfunctions of the boundary value problem are found using the Wronskian
functions. We present an example in order to compare the proposed solution.

Kaynakça

  • S.L. Chang, L.A. Zadeh, On Fuzzy Mapping and Control , IEEE Transactions on Systems Man Cybernetics, Vol. 2, No. 1, pp. 30-34 (1972).
  • M. L. Puri, D. A. Ralescu , Differentials of fuzzy functions, Journal of Math. Analysis and App., Vol. 91, No. 2, pp. 552–558 (1983).
  • O. Kaleva , Fuzzy differential equations, Fuzzy sets and systems, Vol. 24, No. 3, pp. 301–317 (1987).
  • B. Bede, S. G. Gal , Generalizations of the differentiability of fuzzy number-valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems, Vol. 151, pp. 581-599 (2005).
  • N. Gasilov, S.E. Amrahov, A.G. Fatullayev , Solution of linear differential equations with fuzzy boundary values, Fuzzy Sets Syst., Vol. 257, pp. 169–183 (2014).
  • M.T. Mizukoshi, L.C. Barros, Y. Chalco-Cano, H. Rom´an-Flores, R.C. Bassanezi, Fuzzy differential equations and the extension principle, Inf. Sci., Vol. 177, pp. 3627–3635 (2007).
  • H.K. Liu , Comparison results of two-point fuzzy boundary value problems, International Journal of Computational and Mathematical Sciences, Vol. 5, No. 1, pp. 1-7 (2011).
  • H. Gultekin Citil, , The eigenvalues and the eigenfunctions of the Sturm- Liouville fuzzy boundary value problem according to the generalized differentiability, Scholars Journal of Physics, Vol. 4, No. 4, pp. 185–195 (2017).
  • T. Ceylan, N. Altinisik, Eigenvalue problem with fuzzy coefficients of boundary conditions, Scholars Journal of Physics, Mathematics and Statistics, Vol. 5, No. 2, pp. 187–193 (2018).
  • J.J. Buckley, T. Feuring , Fuzzy initial value problem for N-th order linear differential equations, Fuzzy Sets and Systems, Vol. 121, pp. 247–255 (2001).
  • O. Akın, T. Khaniyev, S. Bayeg, I.B. Turksen, Solving a Second Order Fuzzy Initial Value Problem Using The Heaviside Function, Turk. J. Math. Comput. Sci., Vol. 4, pp. 16–25 (2016).
  • G. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic,Prentice Hall Inc., Upper Saddle River, (1995).
  • I. Sadeqi, M. Moradlou, M. Salehi, On approximate cauchy equation in felbin’s type fuzzy normed linear spaces, Iranian Journal of Fuzzy Sys., Vol. 10, No. 3, pp. 51-63 (2013).
  • P. Diamond, P. Kloeden, Metric spaces of fuzzy sets, World Scientific, Singapore, (1994).
  • A. Kandel, W. Byatt, Fuzzy differential equations,Proceedings of the International Conference on Cybernetics and Society,, Tokyo, (1978).
  • L. C. de Barros, R. C. Bassanezi, P. A. Tonelli, On the continuity of the zadeh’s extension, In: Proceedings of Seventh IFSA World Congress, (1977).
  • E. C. Titchmarsh, Eigenfunction expansions associated with second-order differential equations I, 2nd edn., Oxford University Press, London, (1962).
Yıl 2023, Cilt: 6 Sayı: 2, 131 - 141, 31.07.2023
https://doi.org/10.33773/jum.1307156

Öz

Kaynakça

  • S.L. Chang, L.A. Zadeh, On Fuzzy Mapping and Control , IEEE Transactions on Systems Man Cybernetics, Vol. 2, No. 1, pp. 30-34 (1972).
  • M. L. Puri, D. A. Ralescu , Differentials of fuzzy functions, Journal of Math. Analysis and App., Vol. 91, No. 2, pp. 552–558 (1983).
  • O. Kaleva , Fuzzy differential equations, Fuzzy sets and systems, Vol. 24, No. 3, pp. 301–317 (1987).
  • B. Bede, S. G. Gal , Generalizations of the differentiability of fuzzy number-valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems, Vol. 151, pp. 581-599 (2005).
  • N. Gasilov, S.E. Amrahov, A.G. Fatullayev , Solution of linear differential equations with fuzzy boundary values, Fuzzy Sets Syst., Vol. 257, pp. 169–183 (2014).
  • M.T. Mizukoshi, L.C. Barros, Y. Chalco-Cano, H. Rom´an-Flores, R.C. Bassanezi, Fuzzy differential equations and the extension principle, Inf. Sci., Vol. 177, pp. 3627–3635 (2007).
  • H.K. Liu , Comparison results of two-point fuzzy boundary value problems, International Journal of Computational and Mathematical Sciences, Vol. 5, No. 1, pp. 1-7 (2011).
  • H. Gultekin Citil, , The eigenvalues and the eigenfunctions of the Sturm- Liouville fuzzy boundary value problem according to the generalized differentiability, Scholars Journal of Physics, Vol. 4, No. 4, pp. 185–195 (2017).
  • T. Ceylan, N. Altinisik, Eigenvalue problem with fuzzy coefficients of boundary conditions, Scholars Journal of Physics, Mathematics and Statistics, Vol. 5, No. 2, pp. 187–193 (2018).
  • J.J. Buckley, T. Feuring , Fuzzy initial value problem for N-th order linear differential equations, Fuzzy Sets and Systems, Vol. 121, pp. 247–255 (2001).
  • O. Akın, T. Khaniyev, S. Bayeg, I.B. Turksen, Solving a Second Order Fuzzy Initial Value Problem Using The Heaviside Function, Turk. J. Math. Comput. Sci., Vol. 4, pp. 16–25 (2016).
  • G. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic,Prentice Hall Inc., Upper Saddle River, (1995).
  • I. Sadeqi, M. Moradlou, M. Salehi, On approximate cauchy equation in felbin’s type fuzzy normed linear spaces, Iranian Journal of Fuzzy Sys., Vol. 10, No. 3, pp. 51-63 (2013).
  • P. Diamond, P. Kloeden, Metric spaces of fuzzy sets, World Scientific, Singapore, (1994).
  • A. Kandel, W. Byatt, Fuzzy differential equations,Proceedings of the International Conference on Cybernetics and Society,, Tokyo, (1978).
  • L. C. de Barros, R. C. Bassanezi, P. A. Tonelli, On the continuity of the zadeh’s extension, In: Proceedings of Seventh IFSA World Congress, (1977).
  • E. C. Titchmarsh, Eigenfunction expansions associated with second-order differential equations I, 2nd edn., Oxford University Press, London, (1962).
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Tahir Ceylan 0000-0002-3187-2800

Yayımlanma Tarihi 31 Temmuz 2023
Gönderilme Tarihi 30 Mayıs 2023
Kabul Tarihi 28 Temmuz 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 2

Kaynak Göster

APA Ceylan, T. (2023). TWO POINT FUZZY BOUNDARY VALUE PROBLEM WITH EXTENSION PRINCIPLE USING HEAVISIDE FUNCTION. Journal of Universal Mathematics, 6(2), 131-141. https://doi.org/10.33773/jum.1307156
AMA Ceylan T. TWO POINT FUZZY BOUNDARY VALUE PROBLEM WITH EXTENSION PRINCIPLE USING HEAVISIDE FUNCTION. JUM. Temmuz 2023;6(2):131-141. doi:10.33773/jum.1307156
Chicago Ceylan, Tahir. “TWO POINT FUZZY BOUNDARY VALUE PROBLEM WITH EXTENSION PRINCIPLE USING HEAVISIDE FUNCTION”. Journal of Universal Mathematics 6, sy. 2 (Temmuz 2023): 131-41. https://doi.org/10.33773/jum.1307156.
EndNote Ceylan T (01 Temmuz 2023) TWO POINT FUZZY BOUNDARY VALUE PROBLEM WITH EXTENSION PRINCIPLE USING HEAVISIDE FUNCTION. Journal of Universal Mathematics 6 2 131–141.
IEEE T. Ceylan, “TWO POINT FUZZY BOUNDARY VALUE PROBLEM WITH EXTENSION PRINCIPLE USING HEAVISIDE FUNCTION”, JUM, c. 6, sy. 2, ss. 131–141, 2023, doi: 10.33773/jum.1307156.
ISNAD Ceylan, Tahir. “TWO POINT FUZZY BOUNDARY VALUE PROBLEM WITH EXTENSION PRINCIPLE USING HEAVISIDE FUNCTION”. Journal of Universal Mathematics 6/2 (Temmuz 2023), 131-141. https://doi.org/10.33773/jum.1307156.
JAMA Ceylan T. TWO POINT FUZZY BOUNDARY VALUE PROBLEM WITH EXTENSION PRINCIPLE USING HEAVISIDE FUNCTION. JUM. 2023;6:131–141.
MLA Ceylan, Tahir. “TWO POINT FUZZY BOUNDARY VALUE PROBLEM WITH EXTENSION PRINCIPLE USING HEAVISIDE FUNCTION”. Journal of Universal Mathematics, c. 6, sy. 2, 2023, ss. 131-4, doi:10.33773/jum.1307156.
Vancouver Ceylan T. TWO POINT FUZZY BOUNDARY VALUE PROBLEM WITH EXTENSION PRINCIPLE USING HEAVISIDE FUNCTION. JUM. 2023;6(2):131-4.

Cited By

Intuitionistic fuzzy eigenvalue problem
An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
https://doi.org/10.11121/ijocta.1471