Browsing by Author "Nguyen Huu Can"

Now showing 1 - 10 of 10

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: 27
Citation - Scopus: 29
Fractional Order Continuity of a Time Semi-Linear Fractional Diffusion-Wave System
(Elsevier, 2020) Luu Vu Cam Hoan; Karapinar, Erdal; Singh, Jagdev; Ho Duy Binh; Nguyen Huu Can; Nguyen Duc Phuong; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
Citation - WoS: 7
Citation - Scopus: 7
Identifying the Initial Condition for Space-Fractional Sobolev Equation
(Wilmington Scientific Publisher, Llc, 2021) Le Dinh Long; Le Thi Diem Hang; Baleanu, Dumitru; Nguyen Huu Can; Nguyen Hoang Luc; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work, a final value problem for a fractional pseudo-parabolic equation is considered. Firstly, we present the regularity of solution. Secondly, we show that this problem is ill-posed in Hadamard's sense. After that we use the quasi-boundary value regularization method to solve this problem. To show that the proposed theoretical results are appropriate, we present an illustrative numerical example.
Citation - WoS: 19
Citation - Scopus: 23
Identifying the Space Source Term Problem for a Generalization of the Fractional Diffusion Equation With Hyper-Bessel Operator
(Springer, 2020) Le Nhat Huynh; Baleanu, Dumitru; Nguyen Huu Can; Nguyen Hoang Luc; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 20
Citation - Scopus: 23
Inverse Source Problem for Time Fractional Diffusion Equation With Mittag-Leffler Kernel
(Springer, 2020) Nguyen Hoang Luc; Baleanu, Dumitru; Zhou, Yong; Le Dinh Long; Nguyen Huu Can; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 3
Citation - Scopus: 3
On a Kirchhoff Diffusion Equation With Integral Condition
(Springer, 2020) Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen Huu Can; Danh Hua Quoc Nam; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - 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: 66
Citation - Scopus: 64
On Continuity of the Fractional Derivative of the Time-Fractional Semilinear Pseudo-Parabolic Systems
(Springer, 2021) Ho Duy Binh; Nguyen Hoang Luc; Nguyen Huu Can; Karapinar, Erdal; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 10
Citation - Scopus: 10
Recovering the Initial Value for a System of Nonlocal Diffusion Equations With Random Noise on the Measurements
(Wiley, 2021) Tran Thanh Binh; Nguyen Duc Phuong; Baleanu, Dumitru; Nguyen Huu Can; Nguyen Anh Triet; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.