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DEMONSTRATIO MATHEMATICAVol. XLNo 42007M. S. N. Murty, G. Suresh KumarINITIAL A N D BOUNDARY VALUE PROBLEMSFOR FUZZY DIFFERENTIAL EQUATIONSAbstract. This paper deals with the study of existence and uniqueness criteria forinitial and boundary value problems associated with fuzzy differential equations of firstand second order with the help of a modified Lipschitz condition.1. IntroductionThe theory of fuzzy differential equations has attracted much attentionin recent times [8]. Many authors ([3]—[10]) have studied initial and boundary value problems associated with first and second order Fuzzy differentialequations on the metric space (E n , D) of normal fuzzy convex sets with thedistance D given by the supremum of the Hausdorff distance between thecorresponding a - level sets.Recently in [3] they have been obtained existence and uniqueness conditions of solutions for initial value problems associated with nonlinear secondorder and higher order fuzzy differential equations satisfying a Lipschitz condition. In this paper, we prove existence and uniqueness theorems for firstand second order nonlinear fuzzy differential equations satisfying a modifiedLipschitz condition.Section 2 is concerned with notations and terminology relating to fuzzysets and also deals with existence and uniqueness theorem for initial valueproblems associated with first order fuzzy differential equations. In section 3 we prove existence and
Demonstratio Mathematica – de Gruyter
Published: Oct 1, 2007
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