Partial Differential Equations in Applied Mathematics最新文献

Investigation of lump, breather and multi solitonic wave solutions to fractional nonlinear dynamical model with stability analysis 分式非线性动力学模型的肿块波、呼吸波和多孤子波解的研究与稳定性分析

Partial Differential Equations in Applied Mathematics Pub Date : 2024-10-15 DOI: 10.1016/j.padiff.2024.100955

{"title":"Investigation of lump, breather and multi solitonic wave solutions to fractional nonlinear dynamical model with stability analysis","authors":"","doi":"10.1016/j.padiff.2024.100955","DOIUrl":"10.1016/j.padiff.2024.100955","url":null,"abstract":"<div><div>In the current research, the new extended direct algebraic method (NEDAM) and the symbolic computational method, along with different test functions, the Hirota bilinear method, are capitalized to secure soliton and lump solutions to the <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional fractional telecommunication system. Consequently, we derive soliton solutions with sophisticated structures, such as mixed trigonometric, rational, hyperbolic, unique, periodic, dark-bright, bright-dark, and hyperbolic. We also developed a lump-type solution that includes rogue waves and breathers for curiosity’s intellect. These features are important for controlling extreme occurrences in optical communications. Additionally, we investigate modulation instability (MI) in the context of nonlinear optical fibres. Understanding MI is essential for developing systems that may either capitalize on its positive features or mitigate its adverse effects. Also, a comprehensive sensitivity analysis of the observed model is carried out to evaluate the influence of different factors. 3D surfaces and 2D visuals, contours, and density plots of the outcomes are represented with the help of a computer application. Our findings demonstrate the potential of using soliton theory and advanced nonlinear analysis methods to enhance the performance of telecommunication systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An iterative approach for addressing monotone inclusion and fixed point problems with generalized demimetric mappings 解决广义非计量映射的单调包含和定点问题的迭代方法

Partial Differential Equations in Applied Mathematics Pub Date : 2024-10-14 DOI: 10.1016/j.padiff.2024.100953

引用次数: 0

New modifications of natural transform iterative method and q-homotopy analysis method applied to fractional order KDV-Burger and Sawada–Kotera equations 应用于分数阶 KDV-Burger 和 Sawada-Kotera 方程的自然变换迭代法和 q-homotopy 分析法的新修正

Partial Differential Equations in Applied Mathematics Pub Date : 2024-10-11 DOI: 10.1016/j.padiff.2024.100950

引用次数: 0

Existence, stability and the number of two-dimensional invariant manifolds for the convective Cahn–Hilliard equation 对流卡恩-希利亚德方程的存在性、稳定性和二维不变流形数

Partial Differential Equations in Applied Mathematics Pub Date : 2024-10-09 DOI: 10.1016/j.padiff.2024.100946

引用次数: 0

A two-strain COVID-19 co-infection model with strain 1 vaccination 接种 1 号菌株疫苗的双菌株 COVID-19 协同感染模型

Partial Differential Equations in Applied Mathematics Pub Date : 2024-10-09 DOI: 10.1016/j.padiff.2024.100945

{"title":"A two-strain COVID-19 co-infection model with strain 1 vaccination","authors":"","doi":"10.1016/j.padiff.2024.100945","DOIUrl":"10.1016/j.padiff.2024.100945","url":null,"abstract":"<div><div>COVID-19 has caused substantial morbidity and mortality worldwide. Previous models of strain 1 vaccination with re-infection when vaccinated, as well as infection with strain 2 did not consider co-infected classes. To fill this gap, a two co-circulating COVID-19 strains model with strain 1 vaccination, and co-infected is formulated and theoretically analyzed. Sufficient conditions for the stability of the disease-free equilibrium and single-strain 1 and -strain 2 endemic equilibria are obtained. Results show as expected that (1) co-infected classes play a role in the transmission dynamics of the disease (2) a high efficacy vaccine could effectively help mitigate the spread of co-infection with both strain 1 and 2 compared to the low-efficacy vaccine. Sensitivity analysis reveals that the main drivers of the effective reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>e</mi></mrow></msub></math></span> are primarily the effective contact rate for strain 2 (<span><math><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>), the strain 2 recovery rate (<span><math><msub><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>), and the vaccine efficacy or infection reduction due to the vaccine (<span><math><mi>η</mi></math></span>). Thus, implementing intervention measures to mitigate the spread of COVID-19 should not ignore the co-infected individuals who can potentially spread both strains of the disease.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis of boundary layer flow of a Jeffrey fluid over a stretching or shrinking sheet immersed in a porous medium 杰弗里流体在浸入多孔介质的伸缩片上的边界层流动分析

Partial Differential Equations in Applied Mathematics Pub Date : 2024-10-06 DOI: 10.1016/j.padiff.2024.100951

{"title":"Analysis of boundary layer flow of a Jeffrey fluid over a stretching or shrinking sheet immersed in a porous medium","authors":"","doi":"10.1016/j.padiff.2024.100951","DOIUrl":"10.1016/j.padiff.2024.100951","url":null,"abstract":"<div><div>Heat transfer optimization is critical in many applications, such as heat exchangers, electric coolers, solar collectors, and nuclear reactors. The current work looks at the thermohydraulic behavior of Jeffery fluid flow along a plane containing a magnetic field, a non-uniform heat source/sink, and a porous media. Numerical solutions are derived using the Runge-Kutta 4th-order approach and the shooting method. Graphs show how Prandtl number (Pr), thermal stratification (e<sub>1</sub>), Jeffery parameter (λ<sub>1</sub>), porous parameter (λ<sub>2</sub>), magnetic field (M), and heat generation/absorption (γ, a, b) affect velocity and temperature profiles. The results show that thermal stratification increases fluid velocity and temperature, whereas heat source/sink parameters have the reverse effect on heat transfer, and raising the Jeffrey parameter reduces velocity and increases boundary layer thickness. There is extremely high agreement with experimental data from the literature. This work illustrates the utility of hydromagnetic properties in modelling fluid flow over stretching/shrinking sheets in porous media.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A new solution approach to proportion delayed and heat like fractional partial differential equations 比例延迟和类热分式偏微分方程的新求解方法

Partial Differential Equations in Applied Mathematics Pub Date : 2024-10-05 DOI: 10.1016/j.padiff.2024.100948

引用次数: 0

Optimal control strategies for infectious disease management: Integrating differential game theory with the SEIR model 传染病管理的最佳控制策略：将微分博弈论与 SEIR 模型相结合

Partial Differential Equations in Applied Mathematics Pub Date : 2024-10-04 DOI: 10.1016/j.padiff.2024.100943

引用次数: 0

Numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion-wave equations 有效转换机制的数值模拟与分数扩散波方程的收敛分析

Partial Differential Equations in Applied Mathematics Pub Date : 2024-10-03 DOI: 10.1016/j.padiff.2024.100947

{"title":"Numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion-wave equations","authors":"","doi":"10.1016/j.padiff.2024.100947","DOIUrl":"10.1016/j.padiff.2024.100947","url":null,"abstract":"<div><div>In the current study, we solve two very important mathematical models, such as the time fractional-order space-fractional telegraph and diffusion-wave equations using a reliable technique called the Adomian decomposition natural method (ADNM), which combines Adomian decomposition and natural transform. The diffusion wave equation describes the flood wave propagation, which is used in solving overland and open channel flow problems. For this reason, it is critical to fully understand and effectively solve the diffusion wave equations. Because telegraph equations are crucial for modeling and developing voltage or frequency transmission, they are widely used in physics and engineering. Furthermore, the designing process is greatly impacted by the uncertainty in the system parameters. For nonlinear ordinary differential equations based on the theorem of Banach fixed point, we provide existence and uniqueness theorem proofs. The present approach has been successfully used to explore exact solutions for time fractional-order and space fractional-order applications. The results show how effective and valuable the ADNM. This paper presents a methodology that will be used in future work to address similar nonlinear problems related to fractional calculus.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Thermal analysis of hybrid nano-fluids: Modeling and non-similar solutions 混合纳米流体的热分析：建模与非相似解

Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-30 DOI: 10.1016/j.padiff.2024.100944

{"title":"Thermal analysis of hybrid nano-fluids: Modeling and non-similar solutions","authors":"","doi":"10.1016/j.padiff.2024.100944","DOIUrl":"10.1016/j.padiff.2024.100944","url":null,"abstract":"<div><div>The thermal analysis of hybrid nano-fluids is a significant research area with diverse applications in industries such as paint, electronics, and mechanical engineering. Existing literature provides limited solutions to the governing equations for the flow of these fluids. Modeling and deriving non-similar solutions for these equations pose interesting and challenging mathematical problems. This study focuses on investigating heat transfer in the flow of two types of nano-fluids, specifically Al<sub>2O<sub>3/H<sub>2O</sub></sub></sub> micropolar nano-fluid and Al<sub>2</sub>O<sub>3</sub> + Ag/H<sub>2</sub>O hybrid nano-fluid, near an isothermal sphere. Conservation laws are employed to formulate the mathematical problem, and by normalizing the variables, the governing equations are converted into a set of dimensionless partial differential equations. Non-similar solutions are then obtained using numerical methods. A comparative analysis is carried out to assess the influence of various parameters on different profiles and engineering quantities for both types of nano-fluids. Both linear and rotational velocities fall down near the surface of sphere with rising microstructure in hybrid nanofluid. The micro-rotation parameter rises the temperature profile while reduces the Nusselt number of both traditional Al<sub>2</sub>O<sub>3</sub>/water based nanofluid as well as hybrid nanofluid.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0