The relationship between the solutions according to the noniterative method and the generalized differentiability of the fuzzy boundary value problem

Hülya Gültekin Çitil

doi:10.26637/MJM0604/0012

Abstract

In this paper is studied the fuzzy boundary value problem according to the noniterative method and according to the generalized differentiability. Comparison result and relationship between them are given. It is seen on the example.

Keywords:

Two-point fuzzy boundary value problems, Fuzzy differential equation

Mathematics Subject Classification:

Mathematics

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Hülya Gültekin Çitil Department of Mathematics, Faculty of Arts and Sciences, Giresun University, Giresun-28100, Turkey.

Pages: 781-787
Date Published: 01-10-2018
Vol. 6 No. 04 (2018): Malaya Journal of Matematik (MJM)

T. Allahviranloo, M. Chehlabi, Solving fuzzy differential equations based on the length function properties, Soft. Comput., 19 (2015) 307-320.

T. Allahviranloo, K. Khalilpour, A numerical method for two-point fuzzy boundary value problems, World Appl. Sci. J. 13 (10) (2011) 2137-2147.

B. Bede, A note on "two-point boundary value problems associated with non-linear fuzzy differential equations", Fuzzy Sets Syst. 157 (2006) 986-989.

B. Bede, Note on "Numerical solutions of fuzzy differential equations by predictor method", Inf. Sci., 178 (2008), 1917-1922.

B. Bede, S.G. Gal, Generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equation, Fuzzy Sets Syst. 151 (2005) 581-599.

B. Bede, L. Stefanini, Generalized differentiability of fuzzy-valued functions, Fuzzy Sets Syst. 230 (2013) 119 141 .

J.J. Buckley, T. Feuring, Fuzzy differential equations, Fuzzy Sets and Systems, 110 (2000), 43-54.

J.J Buckley, T. Feuring, Fuzzy initial value problem for Nth-order linear differential equation, Fuzzy Sets and Systems, 121 (2001), 247-255.

E. Can, M. A. Bayrak, A new method for solution of fuzzy reaction equation, MATCH Commun. Math. Comput. Chem. 73 (2015) 649-661.

D. Dubois, H. Prade, Operations on fuzzy numbers, Int. J. Syst. Sci. 9 (1978), 613-626.

N.A. Gasilov, S.E. Amrahov, A.G Fatullayev, A geometric approach to solve fuzzy linear systems of differential equations, Appl. Math. Inf. Sci. 5 (2011), 484-495.

X. Guo, D. Shang, X. Lu, Fuzzy approximate solutions of second-order fuzzy linear boundary value problems, Boundary Value Problems, 2013, doi:10.1186/1687-27702013-212.

E. Hüllermeir, An approach to modeling and simulation of uncertain dynamical systems, Internat. J. Uncertanity Fuzziness Knowledge-Based Systems 5 (1997), 117-137.

O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24 (1987), 301-317.

O. Kaleva, The Cauchy problem for fuzzy differential equations, Fuzzy Sets Syst. 35 (1990) 389-396.

A. Khastan, F. Bahrami, K. Ivaz, New results on multiple solutions for Nth-order fuzzy differential equations under generalized differentiability, Boundary Value Problems, doi: $10.1155 / 2009 / 395714,2009$.

A. Khastan, J.J. Nieto, A boundary value problem for second order fuzzy differential equations, Nonlinear Analysis 72 (2010), 3583-3593.

H.K Liu, Comparations results of two-point fuzzy boundary value problems. International Journal of Computational and Mathematical Sciences, 5:1, 2011.

M.L Puri, D.A. Ralescu, Differentials for fuzzy functions, J. Math. Anal. Appl., 91 (1983), 552-558.