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: 12Regularization of the Inverse Problem for Time Fractional Pseudo-Parabolic Equation With Non-Local in Time Conditions(Springer Heidelberg, 2022) Le Dinh Long; Anh Tuan Nguyen; Baleanu, Dumitru; Nguyen Duc Phuong; Long, Le Dinh; Phuong, Nguyen Duc; Nguyen, Anh TuanThis 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.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: 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.