Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 1Citation - Scopus: 1Terminal Value Problem for Stochastic Fractional Equation Within an Operator With Exponential Kernel(World Scientific Publ Co Pte Ltd, 2023) Hoan, Luu Vu Cam; Baleanu, Dumitru; Nguyen, Anh Tuan; Phuong, Nguyen DucIn this paper, we investigate a terminal value problem for stochastic fractional diffusion equations with Caputo-Fabrizio derivative. The stochastic noise we consider here is the white noise taken value in the Hilbert space W. The main contribution is to investigate the well-posedness and ill-posedness of such problem in two distinct cases of the smoothness of the Hilbert scale space W? (see Assumption 3.1), which is a subspace of W. When W? is smooth enough, i.e. the parameter ? is sufficiently large, our problem is well-posed and it has a unique solution in the space of Holder continuous functions. In contract, in the different case when ? is smaller, our problem is ill-posed; therefore, we construct a regularization result.Article Citation - WoS: 4Citation - Scopus: 4Recovering the Source Term for Parabolic Equation With Nonlocal Integral Condition(Wiley, 2021) Baleanu, Dumitru; Tran Thanh Phong; Le Dinh Long; Nguyen Duc Phuong; Thanh Phong, Tran; Duc Phuong, Nguyen; Dinh Long, Le; Long, Le Dinh; Phuong, Nguyen Duc; Phong, Tran ThanhThe 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.Article Citation - WoS: 10Citation - Scopus: 10Recovering 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; Binh, Tran Thanh; Phuong, Nguyen Duc; Can, Nguyen Huu; Triet, Nguyen AnhIn 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.Article Regularized Solution for Nonlinear Elliptic Equations With Random Discrete Data(Wiley, 2019) Nguyen Huy Tuan; Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen Duc Phuong; Duc Phuong, Nguyen; Hoang Luc, Nguyen; Phuong, Nguyen Duc; Tuan, Nguyen Huy; Luc, Nguyen HoangThe 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.Article Citation - WoS: 7Citation - Scopus: 7On 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; Ngoc, Tran Bao; Phuong, Nguyen Duc; Tuan, Nguyen HuyThis 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.