Boundary value problems for semilinear fuzzy impulsive differential inclusions based on semigroups in Banach spaces

Article type: Research Article

Authors: Xiao, Jian-Zhong | Ju, Jia-Min | Jin, Pan-Pan

Affiliations: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, P.R. China

Note: [] Corresponding author. Jian-Zhong Xiao, School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, PR China. Fax: +8602558731073; E-mail: xiaojz@nuist.edu.cn

Abstract: A first-order semilinear fuzzy differential inclusion with fuzzy impulse characteristics and linear boundary conditions is considered in separable Banach spaces. By means of semigroup properties, stacking approach and the fixed point theorem for multivalued map due to Dhage, the existence results for fuzzy solution are established. Some general criteria are presented for a class of semilinear fuzzy differential inclusions including higher dimensional and infinite dimensional uncertain systems, and the conditions for existence of solutions in the results are concise and mild. Also, several examples are given to illustrate the utility and applicability.

Keywords: Fuzzy differential inclusion, fuzzy impulse, semigroup, fixed point for multivalued map, stacking theorem

DOI: 10.3233/IFS-141348

Journal: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 2, pp. 669-680, 2015