Browsing by Author "Hoan, Luu Vu Cam"

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Citation Count: Phuong, Nguyen Duc...et al. (2020). "Fractional order continuity of a time semi-linear fractional diffusion-wave system", Alexandria Engineering Journal, Vol. 59, No. 6, pp. 4959-4968.
Fractional order continuity of a time semi-linear fractional diffusion-wave system
(2020) Phuong, Nguyen Duc; Hoan, Luu Vu Cam; Karapınar, Erdal; Singh, Jagdev; Binh, Ho Duy; Can, Nguyen Huu; 19184
In this work, we consider the time-fractional diffusion equations depend on fractional orders. In more detail, we study on the initial value problems for the time semi-linear fractional diffusion-wave system and discussion about continuity with respect to the fractional derivative order. We find the answer to the question: When the fractional orders get closer, are the corresponding solutions close? To answer this question, we present some depth theories on PDEs and fractional calculus. In addition, we add an example numerical to verify the proposed theory. © 2020
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.