Practical stability of fuzzy differential equations with the second type of Hukuhara derivative

Article type: Research Article

Authors: Zhang, Shuorui | Sun, Jitao^*

Affiliations: Department of Mathematics, Tongji University, Shanghai, China

Correspondence: [*] Correspondence to: Jitao Sun, Department of Mathematics, Tongji University, Shanghai 200092, China. Tel.: +86 21 65983241 1307; Fax: +86 21 65981985; Email: [email protected].

Abstract: In this paper, practical stability of fuzzy differential equations with the second type of Hukuhara derivative are considered. Firstly, some notions are extended to fuzzy differential equations with the second type of Hukuhara derivative. Then with the help of Lyapunov-like functions, sufficient conditions are established for practical stability and practical quasi-stability for a class of fuzzy differential equations with the second type of Hukuhara derivative, respectively. Also, a comparison principle is derived which connects the practical stability relationships between fuzzy differential equations with the second type of Hukuhara derivative and scalar differential equations. Finally some examples are shown to illustrate the effectiveness of the results.

Keywords: Fuzzy differential equations, second type of Hukuhara derivative, practical stability, comparison principle, practically quasi-stable, generalized differentiability

DOI: 10.3233/IFS-151596

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 1, pp. 307-313, 2015