Existence, uniqueness and E_q-Ulam type stability of fuzzy fractional differential equations with parameters¹

Article type: Research Article

Authors: Wang, Yupin | Sun, Shurong^{; *}

Affiliations: School of Mathematical Sciences, University of Jinan, Jinan, Shan dong, P R China

Correspondence: [*] Corresponding author. Shurong Sun, School of Mathematical Sciences, University of Jinan, Jinan 250022, Shan dong, P R China. E-mail: [email protected].

Note: [1] This research is supported by the Natural Science Foundation of China (61703180), and supported by Shan dong Provincial Natural Science Foundation (ZR2016AM17).

Abstract: This paper reports the investigation of the existence and uniqueness of solution to Cauchy problems for a class of nonlinear fuzzy fractional differential equations with the Riemann-Liouville H-derivative. Further, Eq-Ulam type stability results are presented by using direct analysis methods. Finally, several numerical simulations are provided to verify the correctness and effectiveness of the main results.

Keywords: Fuzzy fractional differential equation, initial value problem, strongly generalized Hukuhara differentiability, fractional hyperbolic function, Ulam type stability

DOI: 10.3233/JIFS-181369

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 5533-5545, 2019