Uniqueness and continuous dependence of the solutions of fuzzy delay differential inclusions¹

Article type: Research Article

Authors: Liu, Zhi-bin^a | Tian, Ke-zhong^{a; b} | Wen, Guo-quan^a | Min, Chao^{a; *}

Affiliations: [a] School of Science, Southwest Petroleum University, Chengdu, China | [b] PetroChina Huabei Oilfield Company, Renqiu, China

Correspondence: [*] Corresponding author. Chao Min, School of Science, Southwest Petroleum University, 610500 Chengdu, China. E-mail: minchao@swpu.edu.cn.

Note: [1] This paper is partly supported by the China Scholarship Council, NSFC of China (11526173, 11601451) and the scientific research starting project of SWPU (No. 2015QHZ028).

Abstract: A further discussion about fuzzy delay differential inclusions (FDDIs) is presented in this paper. The uniqueness of the solution of a FDDI is proved under different conditions. And we verify the continuous dependence of the solutions of FDDIs through the Convergence Theorem. The result of this paper is an extension to the study of fuzzy differential inclusions and also suitable for the fuzzy differential equations under certain circumstances. It should be helpful to describe and analyze the dynamic systems of fuzzy uncertainties.

Keywords: Fuzzy delay differential inclusion, fuzzy differential equation, uniqueness of solutions, continuous dependence

DOI: 10.3233/JIFS-162391

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 4, pp. 2171-2176, 2017