Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 10Citation - Scopus: 18Identifying the Space Source Term Problem for Time-Space Diffusion Equation(Springer, 2020) Karapinar, Erdal; Kumar, Devendra; Sakthivel, Rathinasamy; Nguyen Hoang Luc; Can, N. H.; Luc, Nguyen HoangIn this paper, we consider an inverse source problem for the time-space-fractional diffusion equation. Here, in the sense of Hadamard, we prove that the problem is severely ill-posed. By applying the quasi-reversibility regularization method, we propose by this method to solve the problem (1.1). After that, we give an error estimate between the sought solution and regularized solution under a prior parameter choice rule and a posterior parameter choice rule, respectively. Finally, we present a numerical example to find that the proposed method works well.Article Citation - WoS: 9Citation - Scopus: 10Identifying the Source Function for Time Fractional Diffusion With Non-Local in Time Conditions(Springer Heidelberg, 2021) Baleanu, Dumitru; Agarwal, Ravi P.; Long, Le Dinh; Luc, Nguyen HoangThe diffusion equation has many applications in fields such as physics, environment, and fluid mechanics. In this paper, we consider the problem of identifying an unknown source for a time-fractional diffusion equation in a general bounded domain from the nonlocal integral condition. The problem is non-well-posed in the sense of Hadamard, i.e, if the problem has only one solution, the solution will not depend continuously on the input data. To get a stable solution and approximation, we need to offer the regularization methods. The first contribution to the paper is to provide a regularized solution using the modified fractional Landweber method. Two choices are proposed including a priori and a posteriori parameter choice rules, to estimate the convergence rate of the regularized methods. The second new contribution is to use truncation to give an estimate of L-p for the convergence rate.Article Citation - WoS: 7Citation - Scopus: 7Identifying 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; Long, Le Dinh; Luc, Nguyen Hoang; Hang, Le Thi Diem; Can, Nguyen HuuIn 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.Article Citation - WoS: 19Citation - Scopus: 20An Inverse Source Problem for Pseudo-Parabolic Equation With Caputo Derivative(Springer Heidelberg, 2022) Luc, Nguyen Hoang; Tatar, Salih; Baleanu, Dumitru; Can, Nguyen Huu; Long, Le DinhIn 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.Article Citation - WoS: 7Citation - Scopus: 8Determination of Source Term for the Fractional Rayleigh-Stokes Equation With Random Data(Springeropen, 2019) Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen-H Can; Tran Thanh Binh; Binh, Tran Thanh; Luc, Nguyen Hoang; Can, Nguyen-hIn this article, we consider the problem of finding a source term of a Rayleigh-Stokes equation. Our problem is not well-posed in the sense of Hadamard. The sought solution does not depend continuously on the given data. Using the truncation method and some new techniques on trigonometric estimators, we give the regularized solution. Moreover, the mean square error and convergence rates are established.Article Citation - WoS: 20Citation - Scopus: 24Inverse 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; Long, Le Dinh; Can, Nguyen Huu; Luc, Nguyen HoangIn 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.Article Citation - WoS: 19Citation - Scopus: 24Identifying 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; Huynh, Le Nhat; Luc, Nguyen Hoang; Can, Nguyen HuuIn 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.Article Citation - WoS: 5Citation - Scopus: 5A Filter Method for Inverse Nonlinear Sideways Heat Equation(Springer, 2020) O'Regan, Donal; Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen Can; Nguyen Anh Triet; Anh Triet, Nguyen; O’Regan, Donal; Hoang Luc, Nguyen; Luc, Nguyen Hoang; Can, Nguyen; Triet, Nguyen AnhIn this paper, we study a sideways heat equation with a nonlinear source in a bounded domain, in which the Cauchy data at x=X are given and the solution in 0 <= x < X is sought. The problem is severely ill-posed in the sense of Hadamard. Based on the fundamental solution to the sideways heat equation, we propose to solve this problem by the filter method of degree alpha, which generates a well-posed integral equation. Moreover, we show that its solution converges to the exact solution uniformly and strongly in L-p(omega,X; L-2 (R)); omega is an element of[0,X) under a priori assumptions on the exact solution. The proposed regularized method is illustrated by numerical results in the final section.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.