Article
Mathematics, Applied
Chengxin Shi, Hao Cheng, Xiaoxiao Geng
Summary: In this paper, we address the ill-posed backward problem of an inhomogeneous time-fractional diffusion-wave equation in an axis-symmetric cylinder. To achieve stable solutions, we propose an iterative regularization method and derive Holder error estimates using a-priori and a-posteriori parameter choice rules. Numerical examples are provided to validate the effectiveness of our approach.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Xiaoli Feng, Meixia Zhao, Zhi Qian
Summary: This paper addresses the backward problem of a time-space fractional diffusion equation and proposes a Tikhonov regularization method to tackle this ill-posed problem. By utilizing a-priori and a-posteriori regularization parameter choice rules, the method ensures order optimal convergence rates.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Jia Wei He, Yong Zhou
Summary: This paper deals with a backward problem for a nonlinear time fractional wave equation in a bounded domain. By utilizing the properties of Mittag-Leffler functions and the method of eigenvalue expansion, we establish some results about the existence and uniqueness of mild solutions for the proposed problem based on compact technique. Due to the ill-posedness of the backward problem in the sense of Hadamard, a general filter regularization method is used to approximate the solution, and the convergence rate for the regularized solutions is proved.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
(2022)
Article
Mathematics, Applied
Chengxin Shi, Hao Cheng
Summary: This paper focuses on solving the backward problem for the radially symmetric time-fractional diffusion-wave equation under Robin boundary condition. The problem is ill-posed, and an iterative regularization method is applied to solve it. Error estimates are obtained using a priori and a posteriori parameter choice rules. Numerical results demonstrate the efficiency and stability of the proposed method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Dinh Nguyen Duy Hai
Summary: This paper investigates a backward problem for a nonlinear space-fractional diffusion equation with temporally dependent thermal conductivity, showing that the problem is severely ill-posed. By constructing a regularized solution using Fourier transform and a filter function, convergence estimates are explicitly derived for the case of a local Lipschitz reaction term. Special cases of the regularized solution are also presented, extending earlier works on the space-fractional backward diffusion problem.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2021)
Article
Mathematics, Applied
Bin Fan, Mejdi Azaiez, Chuanju Xu
Summary: This paper investigates numerical methods for a backward problem of the time-fractional wave equation in bounded domains. Two fractional filter regularization methods are proposed, which efficiently overcome the well-known over-smoothing drawback caused by classical regularizations. Numerical examples confirm the theoretical results, showing that fractional regularization is more efficient for problems with low regularity.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2021)
Article
Mathematics, Applied
Yao-Qun Wu, Jia Wei He
Summary: This article considers the backward problem for composite fractional relaxation equations using Caputo's fractional derivative. The representation of solutions is established based on a spectral problem, and the maximal regularity for the corresponding initial value problem is shown. Due to the mildly ill-posedness of the current backward problem, the fractional Landweber regularization method is applied to discuss convergence analysis and error estimates.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Chengxin Shi, Hao Cheng, Wenping Fan
Summary: In this paper, the backward problem for a time fractional diffusion-wave equation in a cylinder is considered. The ill-posedness and conditional stability of the inverse problem are proved. An iterative generalized quasi-boundary value regularization method is proposed based on the generalized quasi-boundary value regularization method, which shows a higher convergence rate. The convergence rates of the regularized solution under both a priori and a posteriori regularization parameter choice rules are obtained. Numerical examples demonstrate the effectiveness and stability of the proposed method.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Jin Wen, Zhi-Yuan Li, Yong-Ping Wang
Summary: This paper focuses on solving the backward problem of determining the initial value and initial velocity simultaneously in a time-fractional wave equation, with the help of extra measurement data at two fixed times. The uniqueness of solution is achieved by utilizing the analyticity and asymptotics of the Mittag-Leffler functions under the condition that the two fixed measurement times are sufficiently close. As the problem is ill-posed, a quasi-reversibility method is proposed, with regularization parameters determined by an a priori parameter choice rule. The accuracy and efficiency of the proposed regularization method are demonstrated through several numerical examples in one and two dimensions.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2023)
Article
Mathematics
Yonggang Chen, Yu Qiao, Xiangtuan Xiong
Summary: This study investigates the inverse and ill-posed problem of determining solute concentration for a two-dimensional nonhomogeneous fractional diffusion equation. The model becomes more complex with the presence of a source term. We propose a modified kernel regularization technique for stable numerical reconstruction of the solution, and provide convergence estimates under both a priori and a posteriori parameter choice rules.
Article
Mathematics, Applied
Tran Ngoc Thach, Nguyen Huu Can, Vo Viet Tri
Summary: The main purpose of this paper is to study the problem of recovering a parabolic equation with fractional derivative from its time averaging. By applying the properties of the Mittag-Leffler function, the existence, uniqueness, and regularity of the mild solutions of the proposed problem in some suitable space are established. The ill-posedness of the problem in the sense of Hadamard is also shown, and the convergence rate between the regularized solution and the exact solution in L-p space is derived.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Mian Liu, Chengxin Shi, Hao Cheng
Summary: This paper investigates a backward problem associated with a semi-linear time-fractional heat equation in an axis-symmetric cylinder, which is motivated by the modeling of blast furnace steelmaking in metallurgy. The existence and uniqueness of the solution to the semi-linear problem are established under certain assumptions. Furthermore, the ill-posedness of the backward problem is proven and error estimates are obtained using a generalized quasi-boundary value regularization method. A numerical experiment is presented to demonstrate the effectiveness of the proposed method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Multidisciplinary Sciences
Hongwu Zhang, Yong Lv
Summary: This paper investigates a backward problem of the time-space fractional symmetric diffusion equation with a source term. It provides the existence and uniqueness of the solution and the conditional stability for the inverse problem, and proposes a Galerkin regularization method based on the least squares technique to overcome the ill-posedness of the problem. The method is verified through numerical experiments and shown to work well in dealing with the backward problem of the time-space fractional parabolic equation.
Article
Mathematics
Xiaoli Feng, Lizhi Zhao
Summary: In this paper, a backward problem for the stochastic convection-diffusion equation with source term driven by the fraction Brownian motion is considered. The regularity of the mild solution is illustrated and the instability of the problem is proved. A truncated regularization method is applied to overcome ill-posedness and obtain a stable numerical approximation to u(x, t), with convergence estimates presented under the a-priori parameter choice rule. Numerical experiments are conducted to demonstrate the effectiveness of the regularization method.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2022)
Article
Mathematics, Interdisciplinary Applications
Yonggang Chen, Yu Qiao, Xiangtuan Xiong
Summary: In this article, we investigate a sideways problem of the non-homogeneous time-fractional diffusion equation and obtain conditional stability results. We propose two regularization strategies for solving the inverse problem in the presence of noisy data and prove corresponding error estimates.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Nguyen Huu Can, Devendra Kumar, Tri Vo Viet, Anh Tuan Nguyen
Summary: The main objective of this paper is to study the non-local problem for a pseudo-parabolic equation with fractional time and space. In the first part, the existence and uniformity of the solution are investigated, and the formula for the mild solution and its regularity properties are provided. In the second part, the convergence of the mild solution for the non-local problem to the solution of the local problem is examined when two non-local parameters approach 0. Finally, numerical examples are presented to illustrate the proposed method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Nguyen Huy Tuan, Vo Viet Tri, Jagdev Singh, Tran Ngoc Thach
Summary: In this work, a stochastic Rayleigh-Stokes equation driven by fractional Brownian motion is investigated in different parameter ranges, and the existence, uniqueness, and regularity results of the mild solutions are established.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Chemistry, Applied
Nguyen Quang Hung, Nguyen Thi Hong Anh, Nguyen Sinh Khang, Nguyen Thi Thanh Huong, Nguyen Thi Luyenb, Dang Viet Hau, Nguyen Tien Dat
Summary: The chemical composition and anti-inflammatory activity of the endemic Lysimachia baviensis were studied for the first time in this research. A new stilbene and two new chalcone glycosides were isolated from the methanol extract of L. baviensis. These compounds showed strong inhibition of nitric oxide production in LPS-induced cells.
NATURAL PRODUCT RESEARCH
(2023)
Article
Mathematics, Applied
Ahmet Ocak Akdemir, Ho Duy Binh, Donal O'Regan, Anh Tuan Nguyen
Summary: This paper investigates the Cauchy problem for a fractional diffusion equation in the Caputo type sense. It provides a representation of solutions using Fourier series and analyzes initial value problems for the semi-linear fractional diffusion equation with a memory term. The stability of the fractional derivative order for the time is also discussed under certain assumptions on the input data, using Mittag-Leffler functions, the Banach fixed point theorem, and Sobolev embeddings.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Yong Zhou, Jia Wei He
Summary: This paper generalizes the Ascoli-Arzela theorem and applies it to studying the initial value problem of fractional evolution equations on an infinite interval. By using the Hausdorff theorem, classical/generalized Ascoli-Arzela theorem, Schauder fixed point theorem, Wright function, and Kuratowski measure of noncompactness, we prove the existence of mild solutions on an infinite interval when the semigroup is both compact and noncompact.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Ngoc Tran Bao, Erkan Nane, Nguyen Huy Tuan
Summary: This work investigates the terminal value problem for a stochastic time fractional wave equation. The existence and uniqueness of a mild solution is shown, although time continuity is lacking at t = 0. The inverse problem of recovering the initial value is studied, and it is found that the problem is ill-posed. A truncation regularization method is proposed as a solution.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Plant Sciences
Bui Thi Mai Anh, Do Thi Trang, Hoang Thi Tuyet Lan, Phan Van Kiem, Bui Huu Tai, Nguyen Viet Dung, Ninh Khach Thanh Nam, Nguyen The Cuong, Nguyen Xuan Nhiem, Nguyen Thi Mai
Summary: One new phenylpropanoid glycoside and 13 known compounds were isolated from Tinospora sinensis (Lour.) Merr. The phenylpropanoid glycoside showed significant inhibitory activity against NO production in macrophages. Several other compounds also exhibited moderate NO inhibitory activity.
JOURNAL OF ASIAN NATURAL PRODUCTS RESEARCH
(2023)
Article
Mathematics, Applied
Nguyen Huy Tuan, Nguyen Duc Phuong, Tran Ngoc Thach
Summary: This work considers stochastic Rayleigh-Stokes equations with stochastic terms and delays, and establishes existence and uniqueness results for the mild solution under two different conditions. The study is motivated by a series of papers by T. Caraballo and his colleagues on stochastic differential equations containing delays.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2023)
Article
Clinical Neurology
Bach Xuan Tran, Tham Thi Nguyen, Hao Si Anh Nguyen, Laurent Boyer, Pascal Auquier, Guillaume Fond, Ha Thi Nhi Tran, Hung Manh Nguyen, Jongkwan Choi, Carl A. Latkin, Cyrus S. H. Ho, Syeda F. Husain, Roger S. McIntyre, Melvyn W. B. Zhang, Roger C. M. Ho
Summary: This study evaluated the potential of portable fNIRS as an adjunct diagnostic tool for bipolar and unipolar disorders during cognitive tasks. The study found differences in hemodynamics measured by fNIRS between bipolar and unipolar disorder patients during cognitive tasks. Therefore, assessing hemodynamics using portable fNIRS during cognitive tasks may serve as an adjunct diagnostic tool for mood disorders in low-resource environments.
JOURNAL OF AFFECTIVE DISORDERS
(2023)
Article
Psychiatry
Bach Xuan Tran, Tham Thi Nguyen, Laurent Boyer, Guillaume Fond, Pascal Auquier, Hao Si Anh Nguyen, Ha Thi Nhi Tran, Hung Manh Nguyen, Jongkwan Choi, Huong Thi Le, Carl A. Latkin, Kalpana Isabel Nathan, Syeda F. Husain, Roger S. McIntyre, Cyrus S. H. Ho, Melvyn W. B. Zhang, Roger C. M. Ho
Summary: This study aimed to evaluate the use of a portable fNIRS device as a diagnostic tool for assessing hemodynamics in people with schizophrenia in Vietnam. The results showed that individuals with schizophrenia did not exhibit significant activation in the frontal lobe during cognitive tasks. However, during the Verbal Fluency Test, certain areas of the prefrontal cortex showed promising diagnostic potential for schizophrenia.
FRONTIERS IN PSYCHIATRY
(2023)
Article
Public, Environmental & Occupational Health
Vu Anh Trong Dam, Ha Ngoc Do, Thao Bich Thi Vu, Khanh Long Vu, Hoang Minh Do, Nga Thu Thi Nguyen, Tham Thi Nguyen, Thuc Minh Thi Vu, Thao Phuong Thi Nguyen, Pascal Auquier, Laurent Boyer, Guillaume Fond, Carl A. Latkin, Cyrus S. H. Ho, Roger C. M. Ho
Summary: This study aims to explore the associations of the parent-child relationship, self-esteem, and resilience on the mental wellbeing and satisfaction with life of Vietnamese adolescents. The results showed that factors such as family support and sharing, higher academic performance, self-esteem, and resilience had a positive effect on life satisfaction and mental wellbeing. Female participants had higher satisfaction with life but lower mental wellbeing scores compared to male participants.
FRONTIERS IN PUBLIC HEALTH
(2023)
Article
Health Care Sciences & Services
Quy-Chau Ngo, Lan Phuong Thi Doan, Giap Van Vu, Thu-Phuong Phan, Hanh Thi Chu, Anh Tu Duong, Quan-Hoang Vuong, Manh-Tung Ho, Minh-Hoang Nguyen, Thu-Trang Vuong, Tham Thi Nguyen, Hien Thu Nguyen, Anh Hai Tran Nguyen, Cyrus S. H. Ho, Roger C. M. Ho
Summary: This study examined the satisfaction of smokers who used the QUITLINE service and identified factors associated with their quit attempts and cessation. The results showed that 65.5% of participants were completely satisfied with the counseling service, but the smoking relapse rate was relatively high. The study also found that staff's capacity and motivation were associated with quit attempts and successful cessation, suggesting the need to focus on preventing smoking relapse and strengthening staff training to improve client motivation.
Review
Health Care Sciences & Services
Linh Phuong Doan, Long Hoang Nguyen, Ha Ngoc Do, Tham Thi Nguyen, Giang Thu Vu, Hoa Thi Do, Carl A. Latkin, Roger C. M. Ho, Cyrus S. H. Ho
Summary: This study reviewed recent changes in Vietnam's population policies and assessed the intention of giving birth before 30 in young Vietnamese to provide insights into the potential effectiveness of the policy changes among young people. Results showed that measures relating to age, socioeconomic and biological characteristics, resources of the local health systems, as well as a clean and safe living environment should be incorporated under this policy, implying that further interventions need to be taken into account to cope with delayed childbearing.
Article
Chemistry, Multidisciplinary
Pham Thi Thu Thao, Vo Quoc Trang, Pham Thanh Hai, Nguyen Minh Thong, Nguyen Thi Dong Phuong, Doan Thi Yen Oanh, Pham Cam Nam
Summary: The effect of substituents (Y), including halogen (F and Cl), electron donating (ED), and electron withdrawing (EW) groups, on the thermoparameters and kinetic behavior of reactions between 4Y-ArNH2 and CH3OO center dot was computationally studied. It was found that the electron donating group (ED) reduces the bond dissociation energy (BDE) and ionization energy (IE), and increases the rate of hydrogen transfer reaction of 4Y-ArNH2 and CH3OO center dot.
VIETNAM JOURNAL OF CHEMISTRY
(2023)
Article
Mathematics, Applied
V. Vijayakumar, R. Udhayakumar, Yong Zhou, N. Sakthivel
Summary: The main aim of this article is to focus on the approximate controllability of Sobolev-type fractional control problems in Hilbert spaces without uniqueness. The main results of our article are proved by using the fixed point theorem for multivalued maps with nonconvex values. Moreover, we obtain some results on the continuity of the solution map and the topological structure of the solution set of the considered Sobolev-type fractional differential system.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Manh Tuan Hoang, Matthias Ehrhardt
Summary: In this paper, a simple approach for solving stiff problems is proposed. Through nonlinear approximation and rigorous mathematical analysis, a class of explicit second-order one-step methods with L-stability and second-order convergence are constructed. The proposed methods generalize and improve existing nonstandard explicit integration schemes, and can be extended to higher-order explicit one-step methods.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Jian Liu, Zengqin Zhao
Summary: In this article, we investigate p(x)-biharmonic equations involving Leray-Lions type operators and Hardy potentials. Some new theorems regarding the existence of generalized solutions are reestablished for such equations when the Leray-Lions type operator and the nonlinearity satisfy suitable hypotheses in variable exponent Lebesgue spaces.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Chengcheng Cheng, Rong Yuan
Summary: This paper investigates the spreading dynamics of a nonlocal diffusion KPP model with free boundaries in time almost periodic media. By applying the novel positive time almost periodic function and satisfying the threshold condition for the kernel function, the unique asymptotic spreading speed of the free boundary problem is accurately expressed.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Xia Wang, Xin Meng, Libin Rong
Summary: In this study, a multiscale model incorporating the modes of infection and types of immune responses of HCV is developed. The basic and immune reproduction numbers are derived and five equilibria are identified. The global asymptotic stability of the equilibria is established using Lyapunov functions, highlighting the significant impact of the reproduction numbers on the overall stability of the model.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Junpu Li, Lan Zhang, Shouyu Cai, Na Li
Summary: This research proposes a regularized singular boundary method for quickly calculating the singularity of the special Green's function at origin. By utilizing the special Green's function and the origin intensity factor technique, an explicit intensity factor suitable for three-dimensional ocean dynamics is derived. The method does not involve singular integrals, resulting in improved computational efficiency and accuracy.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Ying Dong, Shuai Zhang, Yichen Zhang
Summary: This paper investigates a 2D chemotaxis-consumption system with rotation and no-flux-Dirichlet boundary conditions. It proves that under certain conditions on the rotation angle, the corresponding initial-boundary value problem has a classical solution that blows up at a finite time.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Shuhan Yao, Qi Hong, Yuezheng Gong
Summary: In this article, an extended quadratic auxiliary variable method is introduced for a droplet liquid film model. The method shows good numerical solvability and accuracy.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Tong Wang, Binxiang Dai
Summary: This paper investigates the spreading speed and traveling wave of an impulsive reaction-diffusion model with non-monotone birth function and age structure, which models the evolution of annually synchronized emergence of adult population with maturation. The result extends the work recently established in Bai, Lou, and Zhao (J. Nonlinear Sci. 2022). Numerical simulations are conducted to illustrate the findings.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Dinghao Zhu, Xiaodong Zhu
Summary: This paper constructs the soliton solutions of the KdV equation with non-zero background using the Riemann-Hilbert approach. The irregular Riemann-Hilbert problem is first constructed by direct and inverse scattering transform, and then regularized by introducing a novel transformation. The residue theorem is applied to derive the multi-soliton solutions at the simple poles of the Riemann-Hilbert problem. In particular, the interaction dynamics of the two-soliton solution are illustrated by considering their evolutions at different time.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Danhua He, Liguang Xu
Summary: This paper investigates the stability of conformable fractional delay differential systems with impulses. By establishing a conformable fractional Halanay inequality, the paper provides sufficient criteria for the conformable exponential stability of the systems.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Fei Sun, Xiaoli Li, Hongxing Rui
Summary: This paper presents a high-order numerical scheme for solving the compressible wormhole propagation problem. The scheme utilizes the fourth-order implicit Runge-Kutta method and the block-centered finite difference method, along with high-order interpolation technique and cut-off approach to achieve high-order and bound-preserving.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Zhijie Du, Huoyuan Duan
Summary: This study analyzes a direct discretization method for computing the eigenvalues of the Maxwell eigenproblem. It utilizes a specific finite element space and the classical variational formulation, and proves the convergence of the obtained finite element solutions.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Hongliang Li, Pingbing Ming
Summary: This paper proposes an asymptotic-preserving finite element method for solving a fourth order singular perturbation problem, which preserves the asymptotic transition of the underlying partial differential equation. The NZT element is analyzed as a representative, and a linear convergence rate is proved for the solution with sharp boundary layer. Numerical examples in two and three dimensions are consistent with the theoretical prediction.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Shuyang Xue, Yongli Song
Summary: This paper investigates the spatiotemporal dynamics of the memory-based diffusion equation driven by memory delay and nonlocal interaction. The nonlocal interaction, characterized by the given Green function, leads to inhomogeneous steady states with any modes. The joint effect of nonlocal interaction and memory delay can result in spatially inhomogeneous Hopf bifurcation and Turing-Hopf bifurcation.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Baoquan Zhou, Ningzhong Shi
Summary: This paper develops a stochastic SEIS epidemic model perturbed by Black-Karasinski process and investigates the impact of random fluctuations on disease outbreak. The results show that random fluctuations facilitate disease outbreak, and a sufficient condition for disease persistence is established.
APPLIED MATHEMATICS LETTERS
(2024)
