Browsing by Author "Nguyen Huy Tuan"

Now showing 1 - 8 of 8

Citation - WoS: 14
Citation - Scopus: 15
Approximate Solution for a 2-D Fractional Differential Equation With Discrete Random Noise
(Pergamon-elsevier Science Ltd, 2020) Baleanu, Dumitru; Tran Ngoc Thach; O'Regan, Donal; Nguyen Huu Can; Nguyen Huy Tuan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. (C) 2020 Elsevier Ltd. All rights reserved.
Citation - WoS: 47
Citation - Scopus: 52
Final Value Problem for Nonlinear Time Fractional Reaction-Diffusion Equation With Discrete Data
(Elsevier, 2020) Baleanu, Dumitru; Tran Ngoc Thach; O'Regan, Donal; Nguyen Huu Can; Nguyen Huy Tuan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. (C) 2020 Elsevier B.V. All rights reserved.
Citation - WoS: 15
Citation - Scopus: 12
On a Backward Problem for Fractional Diffusion Equation With Riemann-Liouville Derivative
(Wiley, 2020) Nguyen Hoang Tuan; Baleanu, Dumitru; Tran Ngoc Thach; Nguyen Huy Tuan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L-2 and H-tau norms is considered and illustrated by numerical example.
Citation - WoS: 31
Citation - Scopus: 33
On a Terminal Value Problem for a Generalization of the Fractional Diffusion Equation With Hyper-Bessel Operator
(Wiley, 2020) Le Nhat Huynh; Baleanu, Dumitru; Nguyen Huu Can; Nguyen Huy Tuan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 7
Citation - Scopus: 7
On Cauchy Problem for Nonlinear Fractional Differential Equation With Random Discrete Data
(Elsevier Science inc, 2019) Nguyen Huy Tuan; Baleanu, Dumitru; Tran Bao Ngoc; Nguyen Duc Phuong; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper is concerned with finding the solution u (x, t) of the Cauchy problem for nonlinear fractional elliptic equation with perturbed input data. This study shows that our forward problem is severely ill-posed in sense of Hadamard. For this ill-posed problem, the trigonometric of non-parametric regression associated with the truncation method is applied to construct a regularized solution. Under prior assumptions for the exact solution, the convergence rate is obtained in both L-2 and H-q (for q > 0) norm. Moreover, the numerical example is also investigated to justify our results. (C) 2019 Elsevier Inc. All rights reserved.
Citation - WoS: 34
Citation - Scopus: 35
On Well-Posedness of the Sub-Diffusion Equation With Conformable Derivative Model
(Elsevier, 2020) Tran Bao Ngoc; Baleanu, Dumitru; O'Regan, Donal; Nguyen Huy Tuan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we study an initial value problem for the time diffusion equation (C)partial derivative(beta)/partial derivative t(beta) u + Au = F, 0 < beta <= 1, on Omega x (0, T), where the time derivative is the conformable derivative. We study the existence and regularity of mild solutions in the following three cases with source term F: F = F (x, t), i.e., linear source term; F = F (u) is nonlinear, globally Lipchitz and uniformly bounded. The results in this case play important roles in numerical analysis. F = F (u) is nonlinear, locally Lipchitz and uniformly bounded. The analysis in this case can be widely applied to many problems such as - Time Ginzburg-Landau equations C partial derivative(beta)u/partial derivative t(beta)+ (-Delta)u = vertical bar u vertical bar(mu-1) u; - Time Burgers equations C partial derivative(beta)u/partial derivative t(beta)-( u center dot del) u + (- Delta)u = 0; etc. (C) 2020 Elsevier B.V. All rights reserved.
Citation - WoS: 20
Regularization of a Terminal Value Problem for Time Fractional Diffusion Equation
(Wiley, 2020) Vo Van Au; Le Dinh Long; Baleanu, Dumitru; Nguyen Huy Tuan; Nguyen Anh Triet; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we study an inverse problem with inhomogeneous source to determine an initial data from the time fractional diffusion equation. In general, this problem is ill-posed in the sense of Hadamard, so the quasi-boundary value method is proposed to solve the problem. In the theoretical results, we propose a priori and a posteriori parameter choice rules and analyze them. Finally, two numerical results in the one-dimensional and two-dimensional case show the evidence of the used regularization method.
Regularized Solution for Nonlinear Elliptic Equations With Random Discrete Data
(Wiley, 2019) Nguyen Huy Tuan; Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen Duc Phuong; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The aim of this paper is to study the Cauchy problem of determining a solution of nonlinear elliptic equations with random discrete data. A study showing that this problem is severely ill posed in the sense of Hadamard, ie, the solution does not depend continuously on the initial data. It is therefore necessary to regularize the in-stable solution of the problem. First, we use the trigonometric of nonparametric regression associated with the truncation method in order to offer the regularized solution. Then, under some presumption on the true solution, we give errors estimates and convergence rate in L-2-norm. A numerical example is also constructed to illustrate the main results.