New Results on Multiple Solutions for Nth-Order Fuzzy Differential Equations under Generalized Differentiability

被引：60
作者：
Khastan, A. [1 ,2 ]
Bahrami, F. [1 ,2 ]
Ivaz, K. [1 ,2 ]
机构：
[1] Univ Tabriz, Dept Appl Math, Tabriz 5166616471, Iran
[2] Univ Tabriz, Res Ctr Ind Math, Tabriz 5166616471, Iran
来源：
BOUNDARY VALUE PROBLEMS | 2009年
关键词：
NUMBER-VALUED FUNCTIONS; CALCULUS;
D O I：
10.1155/2009/395714
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We firstly present a generalized concept of higher-order differentiability for fuzzy functions. Then we interpret Nth-order fuzzy differential equations using this concept. We introduce new definitions of solution to fuzzy differential equations. Some examples are provided for which both the new solutions and the former ones to the fuzzy initial value problems are presented and compared. We present an example of a linear second-order fuzzy differential equation with initial conditions having four different solutions. Copyright (C) 2009 A. Khastan et al.
引用
收藏
页数：13
相关论文
共 17 条
[1]   Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations [J].
Bede, B ;
Gal, SG .
FUZZY SETS AND SYSTEMS, 2005, 151 (03) :581-599
[2]   Almost periodic fuzzy-number-valued functions [J].
Bede, B ;
Gal, SG .
FUZZY SETS AND SYSTEMS, 2004, 147 (03) :385-403
[3]   First order linear fuzzy differential equations under generalized differentiability [J].
Bede, Barnabas ;
Rudas, Imre J. ;
Bencsik, Attila L. .
INFORMATION SCIENCES, 2007, 177 (07) :1648-1662
[4]  
Buckley JJ, 2000, FUZZY SET SYST, V110, P43, DOI 10.1016/S0165-0114(98)00141-9
[5]   Fuzzy initial value problem for Nth-order linear differential equations [J].
Buckley, JJ ;
Feuring, T .
FUZZY SETS AND SYSTEMS, 2001, 121 (02) :247-255
[6]   On new solutions of fuzzy differential equations [J].
Chalco-Cano, Y. ;
Roman-Flores, H. .
CHAOS SOLITONS & FRACTALS, 2008, 38 (01) :112-119
[7]   FUZZY MAPPING AND CONTROL [J].
CHANG, SSL ;
ZADEH, LA .
IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS, 1972, SMC2 (01) :30-&
[8]  
Diamond P., 1994, Metric spaces of fuzzy sets
[9]   TOWARDS FUZZY DIFFERENTIAL-CALCULUS .3. DIFFERENTIATION [J].
DUBOIS, D ;
PRADE, H .
FUZZY SETS AND SYSTEMS, 1982, 8 (03) :225-233
[10]   Initial value problems for higher-order fuzzy differential equations [J].
Georgiou, DN ;
Nieto, JJ ;
Rodríguez-López, R .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (04) :587-600
12