Browsing by Author "Nguyen, Anh Tuan"

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Citation - WoS: 16
Citation - Scopus: 17
On a nonlocal problem for a Caputo time-fractional pseudoparabolic equation
(Wiley, 2021) Nguyen, Anh Tuan; Karapınar, Erdal; Hammouch, Zakia; Karapinar, Erdal; Tuan, Nguyen Huy; 19184; Matematik
In this paper, we consider a class of pseudoparabolic equations with the nonlocal condition and the Caputo derivative. Two cases of problems (1-2) will be studied, which are linear case and nonlinear case. For the first case, we establish the existence, the uniqueness, and some regularity results by using some estimates technique and Sobolev embeddings. Second, the Banach fixed-point theorem will be applied to the nonlinear case to prove the existence and the uniqueness of the mild solution.
Citation - WoS: 0
Citation - Scopus: 0
On the Fractional Diffusion Equation Associated With Exponential Source and Operator With Exponential Kernel
(Asme, 2023) Nguyen, Anh Tuan; Baleanu, Dumitru; Nguyen, Van Tien; Baleanu, Dumitru; Nguyen, Van Thinh; 56389; Matematik
In this paper, we investigate the well-posedness of mild solutions of the time-fractional diffusion equation with an exponential source function and the Caputo-Fabrizio derivative of a fractional order a is an element of ( 0 , 1 ). Some linear estimates of the solution kernels on Hilbert scale spaces are constructed using a spectrum of the Dirichlet Laplacian. Based on the Banach fixed point theorem, the global existence and uniqueness of the small-data mild solution are approved. This work is considered the first study on the time-fractional diffusion equation with a nonlinear function for all common dimensions of 1, 2, and 3.
Citation - WoS: 1
Citation - Scopus: 1
Terminal Value Problem For Stochastic Fractional Equation Within An Operator With Exponential Kernel
(World Scientific Publ Co Pte Ltd, 2023) Phuong, Nguyen Duc; Baleanu, Dumitru; Hoan, Luu Vu Cam; Baleanu, Dumitru; Nguyen, Anh Tuan; 56389; Matematik
In this paper, we investigate a terminal value problem for stochastic fractional diffusion equations with Caputo-Fabrizio derivative. The stochastic noise we consider here is the white noise taken value in the Hilbert space W. The main contribution is to investigate the well-posedness and ill-posedness of such problem in two distinct cases of the smoothness of the Hilbert scale space W? (see Assumption 3.1), which is a subspace of W. When W? is smooth enough, i.e. the parameter ? is sufficiently large, our problem is well-posed and it has a unique solution in the space of Holder continuous functions. In contract, in the different case when ? is smaller, our problem is ill-posed; therefore, we construct a regularization result.