On the stability for the fuzzy initial value problem

Article type: Research Article

Authors: Van Hoa, Ngo^{a; b; 1} | Allahviranloo, Tofigh^{c; 2} | Vu, Ho^{d; e; *}

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 Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey | [d] Institute of Research and Development, Duy Tan University, Danang, Vietnam | [e] Faculty of Natural Sciences, Duy Tan University, Danang, Vietnam

Correspondence: [*] Corresponding author. Ho Vu, Institute of Research and Development, Duy Tan University, Danang 550000, Vietnam. E-mail: hovu1@duytan.edu.vn.

Note: [1] E-mail: ngovanhoa@tdtu.edu.vn.

Note: [2] E-mail: tofigh.allahviranloo@eng.bau.edu.tr.

Abstract: In this paper, we present the Hyers–Ulam stability and Hyers–Ulam-Rassias stability (HU-stability and HUR-stability for short) for fuzzy initial value problem (FIVP) by using fixed point theorem. We improve and extend some known results on the stability for FDEs by dropping some assumptions. Some examples illustrate the theoretical results.

Keywords: HU stability, HUR stability, fuzzy differential equation, uncertainly, fixed point theory

Keywords: 34A12, 45J05

DOI: 10.3233/JIFS-201109

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 5, pp. 7747-7755, 2020