Existence and stability results for quaternion fuzzy fractional differential equations in the sense of Hilfer

Article type: Research Article

Authors: Yang, Zhanpeng^{; *} | Ren, Wenjuan

Affiliations: Key Laboratory of Technology in Geo-spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing, P.R. China

Correspondence: [*] Corresponding author. Zhanpeng Yang, Key Laboratory of Technology in Geo-spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, P.R. China. Tel.: +10 58887208 8209; E-mail: zhanpengyang@mail.ie.ac.cn.

Abstract: We consider the initial value problem of quaternion fuzzy fractional differential equations in the generalized regular fuzzy function space. By the associate space theorem and fixed point theorem, some results on the existence and stability for the solution of the initial value problem are given. By the fixed point method, we also prove the Hyers–Ulam stability for the solution of the abstract Cauchy problem under some suitable conditions.

Keywords: Quaternion fuzzy fractional differential equation, associate space, generalized regular function, Hyers–Ulam stability

DOI: 10.3233/JIFS-171042

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 167-175, 2018