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A SYSTEM OF FIRST-ORDER IMPULSIVE FUZZY DIFFERENTIAL EQUATIONS
Lan, Heng-You The Youngnam Mathematical Society Korea 2008 East Asian mathematical journal Vol.24 No.1
In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.
A SYSTEM OF FIRST-ORDER IMPULSIVE FUZZY DIFFERENTIAL EQUATIONS
Heng-You Lan 영남수학회 2008 East Asian mathematical journal Vol.24 No.1
In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.
Lan, Heng-You 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.25 No.1
In this work, by using Xu's inequality, Nalder's results, the notion of $(A,\;{\eta})-accretive$ mappings and the new resolvent operator technique associated with $(A,\;{\eta})-accretive$ mappings due to Lan et al., we study the existence of solutions for a new class of $(A,\;{\eta})-accretive$ variational inclusion problems with non-accretive set-valued mappings and the convergence of the iterative sequences generated by the algorithms in Banach spaces. Our results are new and extend, improve and unify the corresponding results in this field.
SOLUTIONS OF A CLASS OF COUPLED SYSTEMS OF FUZZY DELAY DIFFERENTIAL EQUATIONS
Yu-ting Wu,Heng-You Lan,Fan Zhang 경남대학교 기초과학연구소 2021 Nonlinear Functional Analysis and Applications Vol.26 No.3
The purpose of this paper is to introduce and study a class of coupled systems of fuzzy delay differential equations involving fuzzy initial values and fuzzy source functions of triangular type. We assume that these initial values and source functions are triangular fuzzy functions and define solutions of the coupled systems as a triangular fuzzy function matrix consisting of real functional matrices. The method of triangular fuzzy function, fractional steps and fuzzy terms separation are used to solve the problems. Furthermore, we prove existence and uniqueness of solution for the considered systems, and then a solution algorithm is proposed. Finally, we present an example to illustrate our main results and give some work that can be done later.