The problem with fuzzy eigenvalue parameter in one of the boundary conditions
In this work, we study the problem with fuzzy eigenvalue parameter in one of the boundary conditions. We find fuzzy eigenvalues of the problem using the Wronskian functions \underline{W}_{\alpha }\left( \lambda \right) and \overline{W}
_{\alpha }\left( \lambda \right). Also, we find eigenfunctions associated with eigenvalues. We draw graphics of eigenfunctions.
[1] Irkin, R., Y1lmaz O(¨)zg¨ur, N., Ta>s, N. (2018).Optimization of lactic acid bacteria viability using fuzzy soft set modelling. An Interna- tional Journal of Optimization and Control: Theories & Applications, 8(2), 266-275.
[2] Karaka>s, E., O(¨)zpalamut>cu, H. (2019). A ge-netic algorithm for fuzzy order acceptance and scheduling problem. An International Journal of Optimization and Control: The- ories & Applications, 9(2), 186-196.
[3] Fulton, C. T. (1977). Two point boundary value problems with eigenvalue parameter contained in the boundary conditions. Proc. Soc. Edinburg, 77A, 293-308.
[4] Binding, P. A., Browne, P. J., Watson, B. A. (2002). Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter, II. Journal of Computa- tional and Applied Mathematics, 148(1), 147- 168.
[5] G¨ultekin C>itil, H., Alt1n1>s1k, N. (2017). On the eigenvalues and the eigenfunctions of the Sturm-Liouville fuzzy boundary value prob- lem. Journal of Mathematical and Computa- tional Science, 7(4), 786-805.
[6] G¨ultekin C>itil, H., Alt1n1>s1k, N. (2018). The examination of eigenvalues and eigenfunc- tions of the Sturm-Liouville fuzzy problem ac- cording to boundary conditions. International Journal of Mathematical Combinatorics, 1, 51-60.
[7] G¨ultekin C>itil, H., Alt1n1>s1k, N. (2018). The eigenvalues and the eigenfunctions of the Sturm-Liouville fuzzy problem with fuzzy co- e伍cient boundary conditions. Journal of Sci- ence and Arts, 4(45), 947-958.
[8] G¨ultekin C>itil, H. (2017). The eigenval- ues and the eigenfunctions of the Sturm- Liouville fuzzy boundary value problem ac- cording to the generalized diferentiability. Scholars Journal of Physics, Mathematics and Statistics, 4(4), 185-195.
[9] Ceylan, T., Alt1n1>s1k, N. (2018). Eigenvalue problem with fuzzy coe伍cients of bound- ary conditions. Scholars Journal of Physics, Mathematics and Statistics, 5(2), 187-193.
[10] G¨ultekin C>itil, H. (2019). Important notes for a fuzzy boundary value problem. Applied Mathematics and Nonlinear Sciences, 4(2), 305–314.
[11] Ceylan, T., Alt1n1>s1k, N. (2018). Fuzzy eigen- value problem with eigenvalue parameter con- tained in the boundary condition. Journal of Science and Arts, 3(44), 589-602.
[12] G¨ultekin C>itil, H. (2019). Sturm-Liouville fuzzy problem with fuzzy eigenvalue param- eter. International Journal of Mathematical Modelling & Computations, 9(3), 187- 195.
[13] Liu, H.-K. (2011). Comparison results of two- point fuzzy boundary value problems. Inter- national Journal of Computational and Math- ematical Sciences, 5(1), 1-7.
[14] Khastan, A., Nieto, J. J. (2010). A boundary value problem for second order fuzzy diferen- tial equations. Nonlinear Analysis, 72, 3583- 3593.
[15] Shirin, S., Saha, G. K. (2011). A new compu- tational methodology to find appropriate so- lutions of fuzzy equations. Mathematical The- ory and Modeling, 2(1), 1-10.
[16] Lakshmikantham, V., Mohapatra, R. N.(2003). Theory of Fuzzy Di erential Equa- tions and Inclusions. Taylor and Francis, Lon- don, New York.
[17] Puri, M. L., Ralescu D. A. (1983). Difer- entials of fuzzy functions. Journal of Mathe- matical Analysis and Applications, 91(2), 552- 558.
[18] Bede, B. (2008). Note on “Numerical solutions of fuzzy diferential equations by predictor-corrector method” . Information Sciences, 178(7), 1917-1922.