Solution of linear differential equations with fuzzy boundary values

Fuzzy Sets and Systems

Volumn 257, Issue , 2014, Pages 169-183

  Gasilov, Nizami ^a   Amrahov, Şahin Emrah ^b   Fatullayev, Afet Golayoglu ^a  

^a BASKENT UNIVERSITY   (Turkey)

^b ANKARA UNIVERSITY   (Turkey)

Author keywords

Fuzzy boundary value problem; Fuzzy differential equation; Fuzzy set; Linear transformation

Indexed keywords

BOUNDARY VALUE PROBLEMS; FUZZY RULES; FUZZY SETS; MATHEMATICAL TRANSFORMATIONS;

CONSTANT COEFFICIENTS; FUZZY BOUNDARY VALUE PROBLEMS; FUZZY DIFFERENTIAL EQUATIONS; FUZZY-VALUED FUNCTION; LINEAR DIFFERENTIAL EQUATION; SECOND-ORDER DIFFERENTIAL EQUATION; TRIANGULAR FUZZY NUMBERS; ZADEH'S EXTENSION PRINCIPLES;

LINEAR TRANSFORMATIONS;

EID: 84908118104     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2013.08.008     Document Type: Article

References (30)

1. T. Allahviranloo, S. Abbasbandy, S. Salahshour, and A. Hakimzadeh A new method for solving fuzzy linear differential equations Computing 92 2011 181 197
2. H. Anton, and C. Rorres Elementary Linear Algebra, Applications Version 9th ed. 2005 John Wiley & Sons
3. P.B. Bailey, L.F. Shampine, and P.E. Waltman Nonlinear Two-Point Boundary Value Problems 1968 Academic Press New York
4. B. Bede A note on "two-point boundary value problems associated with non-linear fuzzy differential equations" Fuzzy Sets Syst. 157 2006 986 989
5. B. Bede, and S.G. Gal Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations Fuzzy Sets Syst. 151 2005 581 599
6. B. Bede, and I.J. Rudas Shooting method for fuzzy two-point boundary value problems Proceedings of the 2012 Annual Meeting of the North American Fuzzy Information Processing Society 2012 1 4
7. B. Bede, I.J. Rudas, and A.L. Bencsik First order linear fuzzy differential equations under generalized differentiability Inf. Sci. 177 2007 1648 1662
8. B. Bede, and L. Stefanini Generalized differentiability of fuzzy-valued functions Fuzzy Sets Syst. 230 2013 119 141
9. J.J. Buckley, and T. Feuring Fuzzy differential equations Fuzzy Sets Syst. 110 2000 43 54
10. J.J. Buckley, and T. Feuring Fuzzy initial value problem for Nth-order linear differential equations Fuzzy Sets Syst. 121 2001 247 255
11. Y. Chalco-Cano, M.A. Rojas-Medar, and H. Román-Flores Sobre ecuaciones diferenciales difusas Bol. Soc. Esp. Mat. Apl. 41 2007 91 99
12. Y. Chalco-Cano, and H. Román-Flores On the new solution of fuzzy differential equations Chaos Solitons Fractals 38 2008 112 119
13. Y. Chalco-Cano, H. Román-Flores, and M.A. Rojas-Medar Fuzzy differential equations with generalized derivative Proceedings of the 27th North American Fuzzy Information Processing Society International Conference 2008 IEEE
14. M. Chen, C. Wu, X. Xue, and G. Liu On fuzzy boundary value problems Inf. Sci. 178 2008 1877 1892
15. N.A. Gasilov, Ş.E. Amrahov, and A.G. Fatullayev A geometric approach to solve fuzzy linear systems of differential equations Appl. Math. Inf. Sci. 5 2011 484 495
16. N. Gasilov, Ş.E. Amrahov, and A.G. Fatullayev Linear differential equations with fuzzy boundary values Proceedings of the 5th International Conference on Application of Information and Communication Technologies 2011 IEEE 696 700
17. R. Goetschel, and W. Voxman Elementary fuzzy calculus Fuzzy Sets Syst. 18 1986 31 43
18. E. Hüllermeier An approach to modeling and simulation of uncertain dynamical systems Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5 1997 117 137
19. R.B. Kearfott Rigorous Global Search: Continuous Problems 1996 Kluwer Academic Publishers Dordrecht
20. A. Khastan, and J.J. Nieto A boundary value problem for second-order fuzzy differential equations Nonlinear Anal. 72 2010 3583 3593
21. A. Khastan, J.J. Nieto, and R. Rodríguez-López Periodic boundary value problems for first-order linear differential equations with uncertainty under generalized differentiability Inf. Sci. 222 2013 544 558
22. D. Li, M. Chen, and X. Xue Two-point boundary value problems of uncertain dynamical systems Fuzzy Sets Syst. 179 2011 50 61
23. H.-K. Liu Comparison results of two-point fuzzy boundary value problems Int. J. Comput. Math. Sci. 5 2011 1 7
24. M. Misukoshi, L.C. Barros, Y. Chalco-Cano, H. Román-Flores, and R.C. Bassanezi Fuzzy differential equations and the extension principle Inf. Sci. 177 2007 3627 3635
25. b 2 Fuzzy Sets Syst. 157 2006 939 951
26. J.J. Nieto, R. Rodríguez-López, and M. Villanueva-Pesqueira Exact solution to the periodic boundary value problem for a first-order linear fuzzy differential equation with impulses Fuzzy Optim. Decis. Mak. 10 2011 323 339
27. D. O'Regan, V. Lakshmikantham, and J. Nieto Initial and boundary value problems for fuzzy differential equations Nonlinear Anal. 54 2003 405 415
28. R. Rodríguez-López On the existence of solutions to periodic boundary value problems for fuzzy linear differential equations Fuzzy Sets Syst. 219 2013 1 6
29. L. Stefanini, and B. Bede Generalized Hukuhara differentiability of interval-valued functions and interval differential equations Nonlinear Anal. 71 2009 1311 1328
30. L. Stefanini, L. Sorini, and M.L. Guerra Parametric representation of fuzzy numbers and application to fuzzy calculus Fuzzy Sets Syst. 157 2006 2423 2455