Variational Iteration Approach for Solving Two-Points Fuzzy Boundary Value Problems
Keywords:
Fuzzy boundary value problem, Variational iteration method, Fuzzy number, Fuzzy differential equationAbstract
The main objective of this paper is to introduce interval two-point fuzzy boundary value problems, in which the fuzziness course when the coefficients of the governing ordinary differential equation and/or the boundary conditions include fuzzy numbers of either triangular or trapezoidal types. Such equations will be solved by introducing the concept of α – level sets, α Î [0,1] to treat the fuzzy ordinary differential equation into two nonfuzzy ordinary differential equations, which correspond to the lower and upper solutions of the interval fuzzy solutions. The well-known variational iteration method has been used to solve two-point fuzzy boundary value problems and linear equations have been examined.
References
Tudu, S.; Mondal, S.P.; Ahmadian, A.; Mahmood, A.K.; Salahshour, S.; Ferrara, M.; “Solution of generalised type – 2 Fuzzy boundary value problem,”. Alexandria Eng. J., 60(2): 2725–2739, 2021.
Zadeh, L.A.; “Fuzzy sets,”. Inf. Control, 8(3): 338–353, 1965.
Dubois, D. ; Prade, H. ; “Operations on fuzzy numbers,”. Int. J. Syst. Sci., 1978.
Press, A.; York, N.; “Fuzzy Sets and Systems : Theory and Applications Competitive Strategies : An Advanced Textbook in Game Theory for Business Students S . H . TIJS University of Nijmegen Nij ’ megen , Netherlands,”. pp.111, 1980.
O’Regan, D. ; Lakshmikantham, V.; Nieto, J.J.; “Initial and boundary value problems for fuzzy differential equations”. Nonlin. Anal. Theo. Meth. Appl., 54(3): 405–415, 2003.
Bede, B.; “A note on ‘two-point boundary value problems associated with non-linear fuzzy differential equations”. Fuzzy Sets Syst., 157(7): 986–989, 2006.
Murty, M.S.N.; Suresh, K.G.; “Initial and boundary value problems for fuzzy differential equations”. Demonstr. Math.,40(4): 827–838, 2007.
Khastan, A.; Nieto, J.J.; “A boundary value problem for second order fuzzy differential equations”. Nonlin. Anal. Theo. Meth. Appl., 72(9–10), 3583–3593, 2010.
Gasilov, N.; Amrahov, Ş.E.; Fatullayev, A.G.; “Solution of linear differential equations with fuzzy boundary values”. Fuzzy Sets Syst., 257: 169–183, 2014.
Saadeh, R.; Al-Smadi, M.; Gumah, G.; Khalil, H.; Khan, R.A.; “Numerical Investigation for Solving Two-Point Fuzzy Boundary Value Problems by Reproducing Kernel Approach”. Appl. Math. Inf. Sci., 10(6): 2117–2129, 2016.
Sagban, H.M.; Fadhel, F.S.; “Approximate Solution of Linear Fuzzy Initial Value Problems Using Modified Variaional Iteration Method”. Al-Nahrain J. Sci., 24(4): 32-39, 2021.
Mahdi, S.R.; “Approximation Method For Solving Fuzzy Differential And Integral Equations” Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Baghdad, 2022.
Wong, C.; “Fuzzy points and local properties of fuzzy topology”. J. Math. Anal. Appl., 46(2), 316–328, 1974.
Klir, B.; Yuan, G.J.; “Fuzzy set theory: Foundations and applications”. 1997.
Rasheed, S.M.; “Approximation Method For Solving Fuzzy Differential And Integral Equations”. Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Baghdad, 2022.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Hussein Razzaq, Fadhel S. Fadhel
This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg)
