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Browsing by Author "Thach, Tran Ngoc"

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    Article
    Approximate Solution for A 2-D Fractional Differential Equation With Discrete Random Noise
    (Elsevier LTD., 2020) Baleanu, Dumitru; Baleanu, Dumitru; Thach, Tran Ngoc; O’Regan, Donal; Can, Nguyen Huu; 56389
    We study a boundary value problem for a 2-D fractional differential equation (FDE) with random noise. This problem is not well-posed. Hence, we use truncated regularization method to establish regularized solutions for the such problem. Finally, the convergence rate of this approximate solution and a numerical example are investigated.
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    Article
    Final value problem for nonlinear time fractional reaction–diffusion equation with discrete data
    (2020) Baleanu, Dumitru; Baleanu, Dumitru; Thach, Tran Ngoc; O'Regan, Donal; Can, Nguyen Huu; 56389
    In this paper, we study the problem of finding the solution of a multi-dimensional time fractional reaction–diffusion equation with nonlinear source from the final value data. We prove that the present problem is not well-posed. Then regularized problems are constructed using the truncated expansion method (in the case of two-dimensional) and the quasi-boundary value method (in the case of multi-dimensional). Finally, convergence rates of the regularized solutions are given and investigated numerically. © 2020 Elsevier B.V.
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    Article
    On a backward problem for fractional diffusion equation with Riemann-Liouville derivative
    (2020) Baleanu, Dumitru; Tuan, Nguyen Hoang; Baleanu, Dumitru; Thach, Tran Ngoc; 56389
    In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L-2 and H-tau norms is considered and illustrated by numerical example.