On the initial value problem for random fuzzy differential equations with Riemann-Liouville fractional derivative: Existence theory and analytical solution

Article type: Research Article

Authors: Vu, Ho^a | An, Truong Vinh^b | Van Hoa, Ngo^{c; d; *}

Affiliations: [a] Faculty of Mathematical Economics, Banking University of Ho Chi Minh City, Vietnam | [b] Faculty of Applied Sciences, University of Technology and Education Ho Chi Minh City, Vietnam | [c] Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam | [d] Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, 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. [email protected].

Abstract: In this paper, the existence and uniqueness results of an initial value problem for random fuzzy differential equations with Riemann-Liouville fractional derivative (RFFDEs) are introduced. A method to find analytical solution of RFFDEs is also proposed. Finally, some initial value problems of linear random fractional fuzzy differential equation and the fish proportional harvesting model in fuzzy environment are given to show the efficiency of the method.

Keywords: Random fractional differential equations, Riemann-Liouville generalized Hukuhara differentiability, Fuzziness and randomness in the fish proportional harvesting model

DOI: 10.3233/JIFS-182876

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 6503-6520, 2019