Browsing by Author "Nguyen Duc Phuong"

Now showing 1 - 7 of 7

Citation - WoS: 2
Citation - Scopus: 2
Fractional evolution equation with Cauchy data in spaces
(Springer, 2022) Nguyen Duc Phuong; Baleanu, Dumitru; Baleanu, Dumitru; Agarwal, Ravi P.; Le Dinh Long; 56389; Matematik
In this paper, we consider the Cauchy problem for fractional evolution equations with the Caputo derivative. This problem is not well posed in the sense of Hadamard. There have been many results on this problem when data is noisy in L-2 and H-s,H- However, there have not been any papers dealing with this problem with observed data in L-p with p not equal 2. We study three cases of source functions: homogeneous case, inhomogeneous case, and nonlinear case. For all of them, we use a truncation method to give an approximate solution to the problem. Under different assumptions on the smoothness of the exact solution, we get error estimates between the regularized solution and the exact solution in L-p. To our knowledge, L-p evaluations for the inverse problem are very limited. This work generalizes some recent results on this problem.
Citation - WoS: 27
Citation - Scopus: 29
Fractional order continuity of a time semi-linear fractional diffusion-wave system
(Elsevier, 2020) Nguyen Duc Phuong; Karapınar, Erdal; Luu Vu Cam Hoan; Karapinar, Erdal; Singh, Jagdev; Ho Duy Binh; Nguyen Huu Can; 19184; Matematik
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
On Cauchy problem for nonlinear fractional differential equation with random discrete data
(Elsevier Science inc, 2019) Nguyen Duc Phuong; Baleanu, Dumitru; Nguyen Huy Tuan; Baleanu, Dumitru; Tran Bao Ngoc; 56389; Matematik
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: 9
Citation - Scopus: 9
Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements
(Wiley, 2021) Nguyen Anh Triet; Baleanu, Dumitru; Tran Thanh Binh; Nguyen Duc Phuong; Baleanu, Dumitru; Nguyen Huu Can; 56389; Matematik
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.
Citation - WoS: 4
Citation - Scopus: 4
Recovering the source term for parabolic equation with nonlocal integral condition
(Wiley, 2021) Nguyen Duc Phuong; Baleanu, Dumitru; Baleanu, Dumitru; Tran Thanh Phong; Le Dinh Long; 56389; Matematik
The main purpose of this article is to present a Tikhonov method to construct the source function f(x) of the parabolic diffusion equation. This problem is well known to be severely ill-posed. Therefore, regularization is required. The error estimates between the sought solution and the regularized solution are obtained under an a priori parameter choice rule and an a posteriori parameter choice rule, respectively. One numerical test illustrates that the proposed method is feasible and effective.
Citation - WoS: 9
Citation - Scopus: 11
Regularization of the Inverse Problem for Time Fractional Pseudo-parabolic Equation with Non-local in Time Conditions
(Springer Heidelberg, 2022) Nguyen Duc Phuong; Baleanu, Dumitru; Le Dinh Long; Anh Tuan Nguyen; Baleanu, Dumitru; 56389; Matematik
This paper is devoted to identifying an unknown source for a time-fractional diffusion equation in a general bounded domain. First, we prove the problem is non-well posed and the stability of the source function. Second, by using the Modified Fractional Landweber method, we present regularization solutions and show the convergence rate between regularization solutions and sought solution are given under a priori and a posteriori choice rules of the regularization parameter, respectively. Finally, we present an illustrative numerical example to test the results of our theory.
Citation - WoS: 0
Citation - Scopus: 0
Regularized solution for nonlinear elliptic equations with random discrete data
(Wiley, 2019) Nguyen Duc Phuong; Baleanu, Dumitru; Nguyen Huy Tuan; Baleanu, Dumitru; Nguyen Hoang Luc; 56389; Matematik
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.