Existence and uniqueness of solutions for random fuzzy fractional integral and differential equations

Article type: Research Article

Authors: Lupulescu, Vasile^a | Dong, Le Si^b | Van Hoa, Ngo^{c; d; *}

Affiliations: [a] Constantin Brancusi University, Republicii 1, Targu-Jiu, Romania | [b] Faculty of Basic Education Banking University, 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. Tel.: +84 908962557; [email protected]

Abstract: In this paper the random fuzzy fractional integral and differential equations are introduced. Under Lipschitz condition we obtain the existence and uniqueness theorems of solutions for two general forms of random fuzzy fractional integral equations. To prove this assertion we use an idea of successive approximations. Moreover, the approach is followed to prove the existence and uniqueness of solutions for random fuzzy fractional initial value problem under Caputo-type fuzzy fractional derivatives. The method is illustrated by solving an example.

Keywords: Fractional differential equations, fuzzy differential equations, random fuzzy fractional differential equation

DOI: 10.3233/IFS-141368

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 1, pp. 27-42, 2015