Global existence and uniqueness of the solution to the impulsive interval-valued differential equations under generalized Hukuhara differentiability

Article type: Research Article

Authors: Dinh Phu, Nguyen^{a; b; *} | Nhut Hung, Nguyen^c | Hoang Giang, Nguyen^c

Affiliations: [a] Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam | [b] Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam | [c] Faculty of Mathematics and Computer Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam

Correspondence: [*] Corresponding author. Nguyen Dinh Phu. E-mail: [email protected].

Abstract: In this work, we presented the global existence and uniqueness of the solution to some classes of the impulsive interval-valued differential equations under generalized Hukuhara differentiability, for example, the impulsive interval-valued differential equations (IIDEs), the linear impulsive interval-valued differential equations (LIIDEs) under generalized Hukuhara differentiability by using the Lyapunov like function, Dini’s derivative and scalar ordinary differential equations.

Keywords: Generalized Hukuhara differentiability, The impulsive interval-valued differential equations, The Lyapunov like function, The Dini’s derivative

DOI: 10.3233/JIFS-181669

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 423-433, 2019