Browsing by Author "Huynh, Le Nhat"

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Citation Count: Luc, Nguyen Hoang...et al. (2020). "Identifying the space source term problem for a generalization of the fractional diffusion equation with hyper-Bessel operator", Advances in Difference Equations, Vol. 2020, No. 1.
Identifying the space source term problem for a generalization of the fractional diffusion equation with hyper-Bessel operator
(2020) Luc, Nguyen Hoang; Huynh, Le Nhat; Baleanu, Dumitru; Can, Nguyen Huu; 56389
In this paper, we consider an inverse problem of identifying the source term for a generalization of the time-fractional diffusion equation, where regularized hyper-Bessel operator is used instead of the time derivative. First, we investigate the existence of our source term; the conditional stability for the inverse source problem is also investigated. Then, we show that the backward problem is ill-posed; the fractional Landweber method and the fractional Tikhonov method are used to deal with this inverse problem, and the regularized solution is also obtained. We present convergence rates for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. Finally, we present a numerical example to illustrate the proposed method.
Citation Count: Tuan, Nguyen Huy...et al. (2020). "On a terminal value problem for a generalization of the fractional diffusion equation with hyper-Bessel operator", Mathematical Methods in the Applied Sciences, Vol. 43, No. 6, pp. 2858-2882.
On a terminal value problem for a generalization of the fractional diffusion equation with hyper-Bessel operator
(2020) Tuan, Nguyen Huy; Huynh, Le Nhat; Baleanu, Dumitru; Can, Nguyen Huu; 56389
In this paper, we consider an inverse problem of recovering the initial value for a generalization of time-fractional diffusion equation, where the time derivative is replaced by a regularized hyper-Bessel operator. First, we investigate the existence and regularity of our terminal value problem. Then we show that the backward problem is ill-posed, and we propose a regularizing scheme using a fractional Tikhonov regularization method. We also present error estimates between the regularized solution and the exact solution using two parameter choice rules.
Citation Count: Huynh, Le Nhat...et al. (2021). "Recovering the space source term for the fractional-diffusion equation with Caputo–Fabrizio derivative", Journal of Inequalities and Applications, Vol. 2021, No. 1.
Recovering the space source term for the fractional-diffusion equation with Caputo–Fabrizio derivative
(2021) Huynh, Le Nhat; Luc, Nguyen Hoang; Baleanu, Dumitru; Long, Le Dinh; 56389
This article is devoted to the study of the source function for the Caputo–Fabrizio time fractional diffusion equation. This new definition of the fractional derivative has no singularity. In other words, the new derivative has a smooth kernel. Here, we investigate the existence of the source term. Through an example, we show that this problem is ill-posed (in the sense of Hadamard), and the fractional Landweber method and the modified quasi-boundary value method are used to deal with this inverse problem and the regularized solution is also obtained. The convergence estimates are addressed for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. In addition, we give a numerical example to illustrate the proposed method.