Browsing by Author "Tran Bao Ngoc"

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Citation - WoS: 7
Citation - Scopus: 7
On Cauchy Problem for Nonlinear Fractional Differential Equation With Random Discrete Data
(Elsevier Science inc, 2019) Nguyen Huy Tuan; Baleanu, Dumitru; Tran Bao Ngoc; Nguyen Duc Phuong; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper is concerned with finding the solution u (x, t) of the Cauchy problem for nonlinear fractional elliptic equation with perturbed input data. This study shows that our forward problem is severely ill-posed in sense of Hadamard. For this ill-posed problem, the trigonometric of non-parametric regression associated with the truncation method is applied to construct a regularized solution. Under prior assumptions for the exact solution, the convergence rate is obtained in both L-2 and H-q (for q > 0) norm. Moreover, the numerical example is also investigated to justify our results. (C) 2019 Elsevier Inc. All rights reserved.
Citation - WoS: 34
Citation - Scopus: 35
On Well-Posedness of the Sub-Diffusion Equation With Conformable Derivative Model
(Elsevier, 2020) Tran Bao Ngoc; Baleanu, Dumitru; O'Regan, Donal; Nguyen Huy Tuan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we study an initial value problem for the time diffusion equation (C)partial derivative(beta)/partial derivative t(beta) u + Au = F, 0 < beta <= 1, on Omega x (0, T), where the time derivative is the conformable derivative. We study the existence and regularity of mild solutions in the following three cases with source term F: F = F (x, t), i.e., linear source term; F = F (u) is nonlinear, globally Lipchitz and uniformly bounded. The results in this case play important roles in numerical analysis. F = F (u) is nonlinear, locally Lipchitz and uniformly bounded. The analysis in this case can be widely applied to many problems such as - Time Ginzburg-Landau equations C partial derivative(beta)u/partial derivative t(beta)+ (-Delta)u = vertical bar u vertical bar(mu-1) u; - Time Burgers equations C partial derivative(beta)u/partial derivative t(beta)-( u center dot del) u + (- Delta)u = 0; etc. (C) 2020 Elsevier B.V. All rights reserved.