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