Browsing by Author "Can, Nguyen Huu"

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Citation Count: Long, Le Dinh...et al. (2021). "An inverse source problem for pseudo-parabolic equation with Caputo derivative", Journal of Applied Mathematics and Computing.
An inverse source problem for pseudo-parabolic equation with Caputo derivative
(2021) Long, Le Dinh; Luc, Nguyen Hoang; Tatar, Salih; Baleanu, Dumitru; Can, Nguyen Huu; 56389
In this paper, we consider an inverse source problem for a fractional pseudo-parabolic equation. We show that the problem is severely ill-posed (in the sense of Hadamard) and the Tikhonov regularization method is proposed to solve the problem. In addition, we present numerical examples to illustrate applicability and accuracy of the proposed method to some extent.
Citation Count: Tuan, N.H...et al. (2020). "Approximate Solution for A 2-D Fractional Differential Equation With Discrete Random Noise",Chaos, Solitons and Fractals, Vol. 133.
Approximate Solution for A 2-D Fractional Differential Equation With Discrete Random Noise
(Elsevier LTD., 2020) Tuan, Nguyen Huy; Baleanu, Dumitru; Thach, Tran Ngoc; O’Regan, Donal; Can, Nguyen Huu; 56389
We study a boundary value problem for a 2-D fractional differential equation (FDE) with random noise. This problem is not well-posed. Hence, we use truncated regularization method to establish regularized solutions for the such problem. Finally, the convergence rate of this approximate solution and a numerical example are investigated.
Citation Count: Tuan, Nguyen Huy...et al. (2020). "Final value problem for nonlinear time fractional reaction–diffusion equation with discrete data", Journal of Computational and Applied Mathematics, Vol. 376.
Final value problem for nonlinear time fractional reaction–diffusion equation with discrete data
(2020) Tuan, Nguyen Huy; Baleanu, Dumitru; Thach, Tran Ngoc; O'Regan, Donal; Can, Nguyen Huu; 56389
In this paper, we study the problem of finding the solution of a multi-dimensional time fractional reaction–diffusion equation with nonlinear source from the final value data. We prove that the present problem is not well-posed. Then regularized problems are constructed using the truncated expansion method (in the case of two-dimensional) and the quasi-boundary value method (in the case of multi-dimensional). Finally, convergence rates of the regularized solutions are given and investigated numerically. © 2020 Elsevier B.V.
Citation Count: Phuong, Nguyen Duc...et al. (2020). "Fractional order continuity of a time semi-linear fractional diffusion-wave system", Alexandria Engineering Journal, Vol. 59, No. 6, pp. 4959-4968.
Fractional order continuity of a time semi-linear fractional diffusion-wave system
(2020) Phuong, Nguyen Duc; Hoan, Luu Vu Cam; Karapınar, Erdal; Singh, Jagdev; Binh, Ho Duy; Can, Nguyen Huu; 19184
In this work, we consider the time-fractional diffusion equations depend on fractional orders. In more detail, we study on the initial value problems for the time semi-linear fractional diffusion-wave system and discussion about continuity with respect to the fractional derivative order. We find the answer to the question: When the fractional orders get closer, are the corresponding solutions close? To answer this question, we present some depth theories on PDEs and fractional calculus. In addition, we add an example numerical to verify the proposed theory. © 2020
Citation Count: Luc, Nguyen Hoang...et al. (2020). "Identifying the space source term problem for a generalization of the fractional diffusion equation with hyper-Bessel operator", Advances in Difference Equations, Vol. 2020, No. 1.
Identifying the space source term problem for a generalization of the fractional diffusion equation with hyper-Bessel operator
(2020) Luc, Nguyen Hoang; Huynh, Le Nhat; Baleanu, Dumitru; Can, Nguyen Huu; 56389
In this paper, we consider an inverse problem of identifying the source term for a generalization of the time-fractional diffusion equation, where regularized hyper-Bessel operator is used instead of the time derivative. First, we investigate the existence of our source term; the conditional stability for the inverse source problem is also investigated. Then, we show that the backward problem is ill-posed; the fractional Landweber method and the fractional Tikhonov method are used to deal with this inverse problem, and the regularized solution is also obtained. We present convergence rates for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. Finally, we present a numerical example to illustrate the proposed method.
Citation Count: Can, Nguyen Huu...et al. (2020). "Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel", Advances in Difference Equations, Vol. 2020, No.1.
Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel
(2020) Can, Nguyen Huu; 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.
Citation Count: Nam, Danh Hua Quoc...et al. (2020). "On a Kirchhoff diffusion equation with integral condition", Advances in Difference Equations, Vol. 2020, No. 1.
On a Kirchhoff diffusion equation with integral condition
(2020) Nam, Danh Hua Quoc; Baleanu, Dumitru; Luc, Nguyen Hoang; Can, Nguyen Huu; 56389
This paper is devoted to Kirchhoff-type parabolic problem with nonlocal integral condition. Our problem has many applications in modeling physical and biological phenomena. The first part of our paper concerns the local existence of the mild solution in Hilbert scales. Our results can be studied into two cases: homogeneous case and inhomogeneous case. In order to overcome difficulties, we applied Banach fixed point theorem and some new techniques on Sobolev spaces. The second part of the paper is to derive the ill-posedness of the mild solution in the sense of Hadamard.
Citation Count: Tuan, Nguyen Huy...et al. (2020). "On a terminal value problem for a generalization of the fractional diffusion equation with hyper-Bessel operator", Mathematical Methods in the Applied Sciences, Vol. 43, No. 6, pp. 2858-2882.
On a terminal value problem for a generalization of the fractional diffusion equation with hyper-Bessel operator
(2020) Tuan, Nguyen Huy; Huynh, Le Nhat; Baleanu, Dumitru; Can, Nguyen Huu; 56389
In this paper, we consider an inverse problem of recovering the initial value for a generalization of time-fractional diffusion equation, where the time derivative is replaced by a regularized hyper-Bessel operator. First, we investigate the existence and regularity of our terminal value problem. Then we show that the backward problem is ill-posed, and we propose a regularizing scheme using a fractional Tikhonov regularization method. We also present error estimates between the regularized solution and the exact solution using two parameter choice rules.
Citation Count: Karapınar, Erdal...et al. (2021). "On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems", Advances in Difference Equations, Vol. 2021, No. 1.
On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems
(2021) Karapınar, Erdal; Binh, Ho Duy; Luc, Nguyen Hoang; Can, Nguyen Huu; 19184
In this work, we study an initial value problem for a system of nonlinear parabolic pseudo equations with Caputo fractional derivative. Here, we discuss the continuity which is related to a fractional order derivative. To overcome some of the difficulties of this problem, we need to evaluate the relevant quantities of the Mittag-Leffler function by constants independent of the derivative order. Moreover, we present an example to illustrate the theory.
Citation Count: Triet, Nguyen Anh...et al. (2021). "Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements", Mathematical Methods in the Applied Sciences, Vol. 44, No. 6, pp. 5188-5209.
Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements
(2021) Triet, Nguyen Anh; Binh, Tran Thanh; Phuong, Nguyen Duc; Baleanu, Dumitru; Can, Nguyen Huu; 56389
In this work, we study the final value problem for a system of parabolic diffusion equations. In which, the final value functions are derived from a random model. This problem is severely ill-posed in the sense of Hadamard. By nonparametric estimation and truncation methods, we offer a new regularized solution. We also investigate an estimate of the error and a convergence rate between a mild solution and its regularized solutions. Finally, some numerical experiments are constructed to confirm the efficiency of the proposed method.