On the fuzzy fractional differential equation with interval Atangana-Baleanu fractional derivative approach

The fuzzy systems with interval approach use an infinite valued parameter in the range of [0,1] as a confidence degree of belief. This parameter makes more complicity but plays the main role in creating the fuzzy solution of the fuzzy systems. In solving process of the model, the Atangana-Baleanu derivative in the fractional case of differential equations has a memory to use all the previous information. Therefore this is as a key point and advantage of using this derivative to reduce the complicity of numerical results in comparison with other known derivatives. In this paper, first, the ABC fractional derivative on fuzzy set-valued functions in parametric interval form is defined. Then it is applied for proving the existence and uniqueness of the solution of fuzzy fractional differential equation with ABC fractional derivative. In general, it is shown that the last interval model is as a coupled system of nonlinear equations. To solve the final system an efficient numerical method called ABC-PI is used. For more illustration, several examples are solved numerically and analyzed by the figures. (C) 2019 Elsevier Ltd. All rights reserved.