Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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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: 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.