期刊：
EUROPEAN JOURNAL OF APPLIED MATHEMATICS,2025年:1-15 ISSN：0956-7925
通讯作者：
Liu, YF
作者机构：
[Ding, Qian; Yu, Jianshe; Liu, Yunfeng] Guangzhou Univ, Ctr Appl Math, Guangzhou, Guangdong, Peoples R China.;[Ding, Qian] Hunan City Univ, Coll Sci, Yiyang, Peoples R China.;[Guo, Zhiming; Liu, Yunfeng] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou, Guangdong, Peoples R China.;[Chen, Yuming] Wilfrid Laurier Univ, Dept Math, Waterloo, ON, Canada.
通讯机构：
[Liu, YF ] G;Guangzhou Univ, Ctr Appl Math, Guangzhou, Guangdong, Peoples R China.;Guangzhou Univ, Sch Math & Informat Sci, Guangzhou, Guangdong, Peoples R China.
关键词：
seasonal change;cyclical human activity;switching dynamical system;periodic solution
摘要：
Seasonal changes and cyclical human activities (such as periodic fishing bans, Wolbachia -based mosquito population control, and school term breaks) have significant impacts on population dynamics. We propose a general switching dynamical model to describe these periodic changes. The existence, uniqueness and stability of positive periodic solutions are thoroughly investigated. The results are stated in terms of an introduced threshold value. To demonstrate their practicability, the obtained results are applied to two biological situations.
摘要：
In this paper, a degenerated reaction-diffusive avian influenza model with logistic source and spatial heterogeneity is proposed. We analyze the global compact attractor of the solution semi-flow of the model using the $ k $-contraction method. Furthermore, the threshold dynamics in terms of the basic reproduction number $ \mathcal{R}_0^{h} $ are investigated. Specifically, if $ \mathcal{R}_0^{h} < 1 $, the infection-free steady state of the system is globally asymptotically stable. If $ \mathcal{R}_0^{h} >1 $, then the endemic equilibrium is uniformly persistent. Finally, numerical simulations are performed to demonstrate the theoretical results.
摘要：
Chemotaxis of mosquito movement has been widely confirmed, but it has rarely been incorporated into infectious disease modeling. This paper proposes a novel mosquito-borne disease model driven by density-suppressed motility and spatial heterogeneity. Via overcoming the difficulties caused by dispersal mechanism and heterogeneity, we establish the global existence and ultimate boundedness of solutions for the model following a priori estimates and the parabolic regularity theory. We define the basic reproduction ratio \(\mathcal {R}_0\) and derive its upper bound \(\tilde {\mathcal {R}}_0\) and lower bound \(\hat {\mathcal {R}}_0\) , and obtain the threshold dynamics of model. Specifically, we prove that the system is uniformly persistent as \(\hat {\mathcal {R}}_0\gt 1\) and the disease will disappear as \(\tilde {\mathcal {R}}_0\lt 1\) by invoking the comparison principle to the corresponding integral system. In the case of spatial homogeneity, the global asymptotic stability of endemic equilibrium is achieved with the aid of a suitable Lyapunov functional and the eigenvalue theory. Numerically, we apply the model to dengue transmission and demonstrate that the chemotaxis of infected mosquitoes may exacerbate the disease in some regions which highlights the impacts of mosquito taxis on the spread of dengue.
期刊：
International Journal of Multiphase Flow,2025年:105502 ISSN：0301-9322
通讯作者：
Xiang Li
作者机构：
[Qiao-Zhong Li] School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212100, China;State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Dalian University of Technology, Dalian 116024, China;[You Li] College of Science, Hunan City University, Yiyang, 413000, China;Advanced Institute for Ocean Research, Southern University of Science and Technology, Shenzhen, 518055, China;Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
通讯机构：
[Xiang Li] A;Advanced Institute for Ocean Research, Southern University of Science and Technology, Shenzhen, 518055, China<&wdkj&>Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
摘要：
This study proposes a generalized conservative phase-field-based simplified multiphase lattice Boltzmann framework for simulation of N-phase flows with immiscible incompressible fluids. In this model, the generalized conservative phase field equations and the hydrodynamics equations are solved by reconstructing solutions within the LB framework with prediction-correction step based on a fractional-step method. Compared to the conventional lattice Boltzmann modeling, the present numerical strategy significantly decreases the number of variables at each grid point, resulting in lower memory consumption that proves particularly advantageous for multiphase systems with N immiscible incompressible fluids. Meanwhile, the framework enables direct implementation of physical boundary conditions without requiring complex transformations between macroscopic constraints and distribution functions. Notably, the model preserves the mesoscopic kinetic fidelity characteristic inherent to the conventional lattice Boltzmann method and integrates robust numerical stability through the matured fractional-step technique and reconstruction strategy. Several numerical experiments, such as three side-by-side stationary droplets, triply concentric droplets system, the morphology of compound droplet and the spreading dynamic of liquid lenses with large density ratios, are conducted to verify the model effectiveness in calculating surface tension and describing the N-phase interfacial dynamic. The model’s capability to handle the multi-physics field coupling is further demonstrated through simulations of electrohydrodynamic deformation of compound droplets, confirming its applicability to complex N-phase systems with interfacial phenomena and external field interactions. Lastly, the present model is employed to study droplet impact on thin liquid films, demonstrating its robustness and versatility in simulating dynamic fluid flow phenomena.
This study proposes a generalized conservative phase-field-based simplified multiphase lattice Boltzmann framework for simulation of N-phase flows with immiscible incompressible fluids. In this model, the generalized conservative phase field equations and the hydrodynamics equations are solved by reconstructing solutions within the LB framework with prediction-correction step based on a fractional-step method. Compared to the conventional lattice Boltzmann modeling, the present numerical strategy significantly decreases the number of variables at each grid point, resulting in lower memory consumption that proves particularly advantageous for multiphase systems with N immiscible incompressible fluids. Meanwhile, the framework enables direct implementation of physical boundary conditions without requiring complex transformations between macroscopic constraints and distribution functions. Notably, the model preserves the mesoscopic kinetic fidelity characteristic inherent to the conventional lattice Boltzmann method and integrates robust numerical stability through the matured fractional-step technique and reconstruction strategy. Several numerical experiments, such as three side-by-side stationary droplets, triply concentric droplets system, the morphology of compound droplet and the spreading dynamic of liquid lenses with large density ratios, are conducted to verify the model effectiveness in calculating surface tension and describing the N-phase interfacial dynamic. The model’s capability to handle the multi-physics field coupling is further demonstrated through simulations of electrohydrodynamic deformation of compound droplets, confirming its applicability to complex N-phase systems with interfacial phenomena and external field interactions. Lastly, the present model is employed to study droplet impact on thin liquid films, demonstrating its robustness and versatility in simulating dynamic fluid flow phenomena.
期刊：
Fractal and Fractional,2025年9(9):615- ISSN：2504-3110
通讯作者：
Zhao, YG;Yan, R
作者机构：
[Zhao, Yige] Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.;[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.
通讯机构：
[Zhao, YG ] U;[Yan, R ] H;Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.;Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.
摘要：
A class of boundary value problems for fractional differential systems involving variable-order derivatives is considered. Such problems can be transformed into some boundary value problems for nonlinear Caputo fractional differential systems. Here, the relations between linear Caputo fractional differential equations and their corresponding linear integral equations are investigated, and the results demonstrate that a proper Lipschitz-type condition is needed for studying nonlinear Caputo fractional differential equations. Then, an existence and uniqueness result is established in some vector subspaces by Banach's fixed-point theorem and parallel to<middle dot>parallel to e norm. In addition, two examples are presented to illustrate the theoretical conclusions.
期刊：
PROCEEDINGS OF THE 36TH CHINESE CONTROL AND DECISION CONFERENCE, CCDC 2024,2024年:250-253 ISSN：1948-9439
通讯作者：
Yan, R
作者机构：
[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.;[Zhao, Yige] Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.
通讯机构：
[Yan, R ] H;Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.
会议名称：
2024 36th Chinese Control and Decision Conference (CCDC)
会议时间：
25 May 2024
会议地点：
Xi'an, China
会议主办单位：
[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.^[Zhao, Yige] Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.
会议论文集名称：
2024 36th Chinese Control and Decision Conference (CCDC)
关键词：
Fractional boundary value problem;Positive solution;phi-Laplacian operator
摘要：
In this paper, a class of boundary value problems of nonlinear fractional differential equations with phi-Laplacian operator is investigated. Based on the Schauder fixed point theorem, a new existence result for positive solutions, in terms of the value of the parameter h is obtained. Finally, an example is given to illustrate the main result.
期刊：
2024 24TH INTERNATIONAL CONFERENCE ON CONTROL, AUTOMATION AND SYSTEMS, ICCAS 2024,2024年:1042-1047 ISSN：2093-7121
通讯作者：
Zhao, YG
作者机构：
[Zhao, Yige; Han, Jing] Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.;[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.
通讯机构：
[Zhao, YG ] U;Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.
会议名称：
2024 24th International Conference on Control, Automation and Systems (ICCAS)
会议时间：
29 October 2024
会议地点：
Jeju, Korea, Republic of
会议主办单位：
[Zhao, Yige;Han, Jing] Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.^[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.
会议论文集名称：
2024 24th International Conference on Control, Automation and Systems (ICCAS)
关键词：
Fractional boundary value problem;Positive solution;phi-Laplacian operator
摘要：
This paper investigates the existence of positive solutions to boundary value problems for nonlinear fractional differential equations with φ-Laplacian operator, which is fundamental to the study of control theory for such problems. Based on fixed point theorems, several new existence results for positive solutions, in terms of the value of parameters h<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>,h<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>,h<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> are obtained. Finally, two examples are given to illustrate the main results.
作者机构：
[Shi, Yao] Hebei Univ Engn, Sch Math & Phys, Handan 056038, Peoples R China.;[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.;[Liu, Tao] Northeastern Univ Qinhuangdao, Sch Math & Stat, Qinhuangdao 066004, Peoples R China.
通讯机构：
[Shi, Y ; Yan, R ] H;Hebei Univ Engn, Sch Math & Phys, Handan 056038, Peoples R China.;Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.
摘要：
In this paper, a high-accuracy conservative implicit algorithm for computing the space fractional coupled Schrödinger–Boussinesq system is constructed. Meanwhile, the conservative nature, a priori boundedness, and solvability of the numerical solution are presented. Then, the proposed algorithm is proved to be second-order convergence in temporal and fourth-order spatial convergence using the discrete energy method. Finally, some numerical experiments validate the effectiveness of the conservative algorithm and confirm the accuracy of the theoretical results for different choices of the fractional-order α.
期刊：
Results in Physics,2024年62:107842 ISSN：2211-3797
通讯作者：
Kamsing Nonlaopon
作者机构：
[Fei Long] College of Science, Hunan City University, Yiyang 413000, PR China;[Shami A.M. Alsallami] Department of Mathematical Sciences, College of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia;[S. Rezaei] Department of Mathematics, Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey;[Kamsing Nonlaopon] Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand;[E.M. Khalil] Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
通讯机构：
[Kamsing Nonlaopon] D;Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
期刊：
TURKISH JOURNAL OF MATHEMATICS,2024年48(4):645-657 ISSN：1300-0098
通讯作者：
Yan, R
作者机构：
[Leng, Xuan; Yan, Rian; Li, Yabing] Hunan City Univ, Sch Math & Comp Sci, Yiyang, Peoples R China.;[Zhao, Yige] Univ Jinan, Sch Math Sci, Jinan, Peoples R China.
通讯机构：
[Yan, R ] H;Hunan City Univ, Sch Math & Comp Sci, Yiyang, Peoples R China.
关键词：
Caputo fractional derivatives;sign-changing Green's function;fixed point theorem
摘要：
In this paper, Caputo boundary value problems of order 3 < zeta <= 4 are investigated on the interval [0 , 1] . By Guo-Krasnoselskii fixed point theorem, some criteria of existence and multiplicity of positive and decreasing solutions are established. The main novelty of the paper lies in its capability to achieve positive solutions while the corresponding Green's function changes sign. Finally, two examples are provided to illustrate the application of these results.
