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Browsing by Author "Binh, Tran Thanh"

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    Determination of source term for the fractional Rayleigh-Stokes equation with random data
    (2019) Baleanu, Dumitru; Baleanu, Dumitru; Luc, Nguyen Hoang; Can, Nguyen-H; 56389
    In 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.
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    Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements
    (2021) Baleanu, Dumitru; Binh, Tran Thanh; Phuong, Nguyen Duc; Baleanu, Dumitru; Can, Nguyen Huu; 56389
    In 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.