Existence of extremal solutions for interval-valued functional integro-differential equations

Article type: Research Article

Authors: Quang, Le Thanh^a | Hoa, Ngo Van^{b; c; *} | Phu, Nguyen Dinh^a | Tung, Tran Thanh^d

Affiliations: [a] Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam | [b] Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam | [c] Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam | [d] Faculty of Natural Science and Technology, Tay Nguyen University, Buon Ma Thuot City, DakLak Province, Vietnam

Correspondence: [*] Corresponding author. Ngo Van Hoa, Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam. Tel.: +84 908962557; E-mail: ngovanhoa@tdt.edu.vn.

Abstract: This paper is devoted to studying the maximal and minimal solutions for the interval-valued functional integro-differential equations (IFIDEs) under generalized Hukuhara differentiability by the method of upper and lower solutions and monotone iterative technique. Some examples are given to illustrate the results.

Keywords: Interval-valued differential equations, functional integro-differential equations, method of upper and lower solutions, extremal solutions

DOI: 10.3233/IFS-162096

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 6, pp. 3495-3512, 2016