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Fuzzy fractional differential equations with the generalized Atangana-Baleanu fractional derivative

Authors: 

Ho Vu, Behzad Ghanbari, Ngo Van Hoa

Source title: 
Fuzzy Sets and Systems, 429: 1-27, 2022 (ISI)
Academic year of acceptance: 
2021-2022
Abstract: 

In this paper, we introduce a generalization of Atangana-Baleanu type fractional calculus with respect to the generalized Mittag-Leffler kernel which has been named as the generalized Atangana-Baleanu (GAB) type fractional calculus. Existence and uniqueness results for the initial value problems of fuzzy differential equations involving a GAB fractional derivative in the Caputo sense are established by employing the method of successive approximation and by means of fixed point theorems. To visualize the theoretical results, some examples and numerical simulations are given.