Browsing by Author "Zhou, Yong"

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A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
(Elsevier, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Nieto, Juan J.; Torres, Delfim F. M.; Zhou, Yong; 56389
We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered. (C) 2017 Elsevier B.V. All rights reserved.
Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel
(2020) Baleanu, Dumitru; Luc, Nguyen Hoang; Baleanu, Dumitru; Zhou, Yong; Long, Le Dinh; 56389
In this work, we study the problem to identify an unknown source term for the Atangana-Baleanu fractional derivative. In general, the problem is severely ill-posed in the sense of Hadamard. We have applied the generalized Tikhonov method to regularize the instable solution of the problem. In the theoretical result, we show the error estimate between the regularized and exact solutions with a priori parameter choice rules. We present a numerical example to illustrate the theoretical result. According to this example, we show that the proposed regularization method is converged.
On a problem for the nonlinear diffusion equation with conformable time derivative
(2022) Baleanu, Dumitru; Baleanu, Dumitru; Zhou, Yong; Huu Can, Nguyen; 56389
In this paper, we study a nonlinear diffusion equation with conformable derivative: (Formula presented.), where (Formula presented.). We consider both of the problems: Initial value problem: the solution contains the integral (Formula presented.) (critical as (Formula presented.)). Final value problem: not well-posed (if the solution exists it does not depend continuously on the given data). For the initial value problem, the lack of convergence of the integral I, for (Formula presented.). The existence for the solution is represented. For the final value problem, the Hadamard instability occurs, we propose two regularization methods to solve the nonlinear problem in case the source term is a Lipschitz function. The results of existence, uniqueness and stability of the regularized problem are obtained. We also develop some new techniques on functional analysis to propose regularity estimates of regularized solution.