Existence and uniqueness theorems for complex fuzzy differential equation

Article type: Research Article

Authors: You, Cuilian^{; *} | Zhang, Ruili

Affiliations: College of Mathematics and Information Science, Hebei University, Baoding, China

Correspondence: [*] Corresponding author. Cuilian You, College of Mathematics and Information Science, Hebei University, Baoding 071002, China. Tel.: +8615933955927; Fax: +8603123168912; E-mail: [email protected].

Abstract: The theory of fuzzy differential equation has been studied by many researchers. In this paper, the fuzzy differential equation is a different type of differential equations, its fuzziness is not only in the initial conditions and coefficients, but also in the driven process. This paper presents some methods to solve linear complex fuzzy differential equations, and proves some existence and uniqueness theorems of solution for complex fuzzy differential equations based on Lipschitz condition and linear growth condition.

Keywords: Fuzzy variable, fuzzy integral, fuzzy differential, fuzzy differential equation, existence and uniqueness theorem

DOI: 10.3233/JIFS-171231

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 4, pp. 2213-2222, 2018