Browsing by Author "Phuong, Nguyen Duc"

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Citation - WoS: 2
Citation - Scopus: 2
Fractional Evolution Equation With Cauchy Data in L^p Spaces
(Springer, 2022) Baleanu, Dumitru; Agarwal, Ravi P.; Le Dinh Long; Nguyen Duc Phuong; Long, Le Dinh; Phuong, Nguyen Duc
In this paper, we consider the Cauchy problem for fractional evolution equations with the Caputo derivative. This problem is not well posed in the sense of Hadamard. There have been many results on this problem when data is noisy in L-2 and H-s,H- However, there have not been any papers dealing with this problem with observed data in L-p with p not equal 2. We study three cases of source functions: homogeneous case, inhomogeneous case, and nonlinear case. For all of them, we use a truncation method to give an approximate solution to the problem. Under different assumptions on the smoothness of the exact solution, we get error estimates between the regularized solution and the exact solution in L-p. To our knowledge, L-p evaluations for the inverse problem are very limited. This work generalizes some recent results on this problem.
Citation - WoS: 10
Citation - Scopus: 12
Regularization of the Inverse Problem for Time Fractional Pseudo-Parabolic Equation With Non-Local in Time Conditions
(Springer Heidelberg, 2022) Le Dinh Long; Anh Tuan Nguyen; Baleanu, Dumitru; Nguyen Duc Phuong; Long, Le Dinh; Phuong, Nguyen Duc; Nguyen, Anh Tuan
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 - 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) Hoan, Luu Vu Cam; Baleanu, Dumitru; Nguyen, Anh Tuan; Phuong, Nguyen Duc
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.