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

Year 2023, , 131 - 141, 31.07.2023
https://doi.org/10.33773/jum.1307156

Abstract

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.

References

  • 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).
Year 2023, , 131 - 141, 31.07.2023
https://doi.org/10.33773/jum.1307156

Abstract

References

  • 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).
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Tahir Ceylan 0000-0002-3187-2800

Publication Date July 31, 2023
Submission Date May 30, 2023
Acceptance Date July 28, 2023
Published in Issue Year 2023

Cite

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. July 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, no. 2 (July 2023): 131-41. https://doi.org/10.33773/jum.1307156.
EndNote Ceylan T (July 1, 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, vol. 6, no. 2, pp. 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 (July 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, vol. 6, no. 2, 2023, pp. 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.

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