Browsing by Author "Nguyen, Anh Tuan"

Now showing 1 - 5 of 5

Citation Count: Baleanu, Dumitru; Binh, Ho Duy; Nguyen, Anh Tuan. (2022). "On a Fractional Parabolic Equation with Regularized Hyper-Bessel Operator and Exponential Nonlinearities", Symmetry, Vol.14, no.7.
On a Fractional Parabolic Equation with Regularized Hyper-Bessel Operator and Exponential Nonlinearities
(2022) Baleanu, Dumitru; Binh, Ho Duy; Nguyen, Anh Tuan; 56389
Recent decades have witnessed the emergence of interesting models of fractional partial differential equations. In the current work, a class of parabolic equations with regularized Hyper-Bessel derivative and the exponential source is investigated. More specifically, we examine the existence and uniqueness of mild solutions in Hilbert scale-spaces which are constructed by a uniformly elliptic symmetry operator on a smooth bounded domain. Our main argument is based on the Banach principle argument. In order to achieve the necessary and sufficient requirements of this argument, we have smoothly combined the application of the Fourier series supportively represented by Mittag-Leffler functions, with Hilbert spaces and Sobolev embeddings. Because of the presence of the fractional operator, we face many challenges in handling proper integrals which appear in the representation of mild solutions. Besides, the source term of an exponential type also causes trouble for us when deriving the desired results. Therefore, powerful embeddings are used to limit the growth of nonlinearity.
Citation Count: Nguyen, Anh Tuan...et al. (2021). "On a nonlocal problem for a Caputo time-fractional pseudoparabolic equation", Mathematical Methods in the Applied Sciences, Vol. 44, No. 18, pp. 14791-14806.
On a nonlocal problem for a Caputo time-fractional pseudoparabolic equation
(2021) Nguyen, Anh Tuan; Hammouch, Zakia; Karapınar, Erdal; Tuan, Nguyen Huy; 19184
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 Count: Nguyen, Anh Tuan;...et.al. (2023). "On the Fractional Diffusion Equation Associated With Exponential Source and Operator With Exponential Kernel", Journal Of Computational And Nonlinear Dynamics, Vol.18, No.5.
On the Fractional Diffusion Equation Associated With Exponential Source and Operator With Exponential Kernel
(2023) Nguyen, Anh Tuan; Nguyen, Van Tien; Baleanu, Dumitru; Nguyen, Van Thinh; 56389
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 Count: Phuong, Nguyen Duc;...et.al. (2022). "Regularization of the Inverse Problem for Time Fractional Pseudo-parabolic Equation with Non-local in Time Conditions", Acta Mathematica Sinica, English Series, Vol.38, No.12, pp.2199-2219.
Regularization of the Inverse Problem for Time Fractional Pseudo-parabolic Equation with Non-local in Time Conditions
(2022) Phuong, Nguyen Duc; Long, Le Dinh; Nguyen, Anh Tuan; Baleanu, Dumitru; 56389
This paper is devoted to identifying an unknown source for a time-fractional diffusion equation in a general bounded domain. First, we prove the problem is non-well posed and the stability of the source function. Second, by using the Modified Fractional Landweber method, we present regularization solutions and show the convergence rate between regularization solutions and sought solution are given under a priori and a posteriori choice rules of the regularization parameter, respectively. Finally, we present an illustrative numerical example to test the results of our theory.
Citation Count: Phuong, Nguyen Duc;...et.al. (2023). "Terminal Value Problem For Stochastic Fractional Equation Within An Operator With Exponential Kernel", Fractals, Vol.31, No.4.
Terminal Value Problem For Stochastic Fractional Equation Within An Operator With Exponential Kernel
(2023) Phuong, Nguyen Duc; Hoan, Luu Vu Cam; Baleanu, Dumitru; Nguyen, Anh Tuan; 56389
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 Wν (see Assumption 3.1), which is a subspace of W. When Wν is smooth enough, i.e. the parameter ν is sufficiently large, our problem is well-posed and it has a unique solution in the space of Hölder continuous functions. In contract, in the different case when ν is smaller, our problem is ill-posed; therefore, we construct a regularization result.