Partial Differential Equations in Applied Mathematics最新文献_第3页

The modeling and mathematical analysis of the fractional-order of Cholera disease: Dynamical and Simulation 霍乱疾病分数阶的建模和数学分析：动态和模拟

Partial Differential Equations in Applied Mathematics Pub Date : 2024-11-12 DOI: 10.1016/j.padiff.2024.100978

Rasha M. Yaseen , Nidal F. Ali , Ahmed A. Mohsen , Aziz Khan , Thabet Abdeljawad

引用次数: 0

Comparative analysis on the radiative time-dependent water/kerosene-based Cu nanofluid through squeezing Riga plates with heat dissipation: Spectral quasilinearization technique 通过具有散热功能的挤压里加板对辐射时间依赖性水/煤油基铜纳米流体进行比较分析：光谱准线性化技术

Partial Differential Equations in Applied Mathematics Pub Date : 2024-11-12 DOI: 10.1016/j.padiff.2024.100988

Subhajit Panda , Titilayo M Agbaje , Rupa Baithalu , S.R. Mishra

{"title":"Comparative analysis on the radiative time-dependent water/kerosene-based Cu nanofluid through squeezing Riga plates with heat dissipation: Spectral quasilinearization technique","authors":"Subhajit Panda , Titilayo M Agbaje , Rupa Baithalu , S.R. Mishra","doi":"10.1016/j.padiff.2024.100988","DOIUrl":"10.1016/j.padiff.2024.100988","url":null,"abstract":"<div><div>The time-dependent thermal management along with convective flows are vital in various heat transfer applications in engineering systems such as in automotive cooling systems, and industrial heat exchangers. Because of enhanced thermal conductivity, nanofluids are widely considered for advanced cooling systems such as electronics, aerospace, geothermal energy extraction, etc. The current analysis presents comparative results of the radiative, time-dependent flow of water/kerosene-based Copper nanofluids between squeezing Riga plates focusing on heat dissipation. Both the plates are embedded within a porous matrix and the influence of non-uniform heat source/sink and thermal convective boundary conditions is examined. Riga plates, generally utilized for their ability to generate electromagnetic fields provide greater control over the fluid flow. The problem designed with the inclusion of aforesaid factors is transformed into a non-dimensional form for the utilization of appropriate similarity functions. Further, the impacts of several effective terms on the flow profiles are presented followed by the numerical solution of the profile obtained using the spectral quasilinearization method. Moreover, some of the outstanding findings are; an increase in the fluid velocity is marked for the separation of the plates but the rate of enhancement in the case of kerosene is more pronounced than that of water. Further, irrespective to the type of fluids, the heat transfer rate enhances for the increasing heat fluid which provides the variation of thermal radiation.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100988"},"PeriodicalIF":0.0,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698761","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

Ginzburg–Landau equations involving different effects and their solitary waves 涉及不同效应的金兹堡-朗道方程及其孤波

Partial Differential Equations in Applied Mathematics Pub Date : 2024-11-12 DOI: 10.1016/j.padiff.2024.100987

K. Hosseini , F. Alizadeh , S. Kheybari , E. Hinçal , B. Kaymakamzade , M.S. Osman

引用次数: 0

Synergistic influence of gyrotactic microorganisms and bimolecular reaction on bidirectional tangent hyperbolic fluid with Nield boundary conditions: A biomathematical model 具有尼尔德边界条件的双向切线双曲流体上的回旋微生物和双分子反应的协同影响：生物数学模型

Partial Differential Equations in Applied Mathematics Pub Date : 2024-11-12 DOI: 10.1016/j.padiff.2024.100994

Subhajit Panda , B. Nayak , Rupa Baithalu , S.R. Mishra

{"title":"Synergistic influence of gyrotactic microorganisms and bimolecular reaction on bidirectional tangent hyperbolic fluid with Nield boundary conditions: A biomathematical model","authors":"Subhajit Panda , B. Nayak , Rupa Baithalu , S.R. Mishra","doi":"10.1016/j.padiff.2024.100994","DOIUrl":"10.1016/j.padiff.2024.100994","url":null,"abstract":"<div><div>In biomedical engineering, the behavior of gyrotactic microorganisms with non-Newtonian fluids such as tangent hyperbolic fluids improve the design of targeted drug delivery systems. In this system control over microorganism movement is essential. The present study deals with the synergistic influence of gyrotactic microorganisms and bimolecular reactions on the bidirectional flow of tangent hyperbolic fluids under Nield boundary conditions. Further, the flow characteristic of the non-Newtonian fluid is enhanced by incorporating the impact of thermal radiation, heat sources, Brownian motion, and thermophoresis. The presentation of these phenomena is vital for an extensive range of applications, including industrial processes, biomedical engineering, and environmental management. The analysis employs advanced mathematical modeling which needs suitable transformation rules to get the non-dimensional form and further numerical simulation is presented with the assistance of the “shooting-based fourth-order Runge–Kutta technique”. The results are depicted for the several contributing factors via the built- in-house function bvp4c in “MATLAB”. The authentication of the study with the prior research is a benchmark to precede further research in this direction. However, the outstanding results are; the fluid velocity is controlled by increasing non-Newtonian Weissenberg number whereas the velocity slip shows dual characteristics on the axial velocity distribution. Further, the motile microorganism profile is controlled by the enhanced bioconvection Lewis number.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100994"},"PeriodicalIF":0.0,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698706","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

Significant properties of AA7075-methanol nanofluid flow through diverging channel with porous material: Differential transform method AA7075-甲醇纳米流体流经多孔材料发散通道的显著特性：微分变换法

Partial Differential Equations in Applied Mathematics Pub Date : 2024-11-10 DOI: 10.1016/j.padiff.2024.100993

R.K. Sahoo , S.R. Mishra , Subhajit Panda

{"title":"Significant properties of AA7075-methanol nanofluid flow through diverging channel with porous material: Differential transform method","authors":"R.K. Sahoo , S.R. Mishra , Subhajit Panda","doi":"10.1016/j.padiff.2024.100993","DOIUrl":"10.1016/j.padiff.2024.100993","url":null,"abstract":"<div><div>The recent industrial needs for the production process depending upon heat transfer properties of the fluids. However, the utility of the nanofluid in comparison to the conventional fluid is widely used because of its advanced coolant efficiency. In particular cooling of electronic devices, drug delivery systems, operation theatre, etc. the use of nanofluid shows its influential characteristics. As a result, the contemporary study aims to inspect the heat transmission effects of alloy nanoparticles via the base fluid methanol is presented through a diverging channel. Particularly, the aluminium alloy of AA7075 containing base metal Aluminium (Al) about 87.1–91.4 %, Zinc (Zn) up to 5.1–6.1 %, Magnesium (Mg) about 2.1–2.9 %, Copper (Cu) within the range of 1.2–2.0 %, Chromium (Cr) amounts 0.18–0.28 %, Silicon (Si) usually <0.4 %, Iron (Fe) <0.5 %, Manganese (Mn) up to 0.3 %, and Titanium (Ti) usually <0.2 %. However, the flow through a permeable medium, the interaction of Darcy dissipation energies the flow phenomena. An appropriate similarity transform rule is employed for the transformation of the basic equations and solved analytically via the differential transform method (DTM). Further, a comparative analysis with previously establish outputs is presented to ensure the accuracy of the adopted methodology. The impact of characterizing factors on the flow profiles are presented graphically and the important outcomes are; the velocity profile shows its dual characteristic for the variation of alloy nanoparticles whereas the fluid temperature enhances significantly. Further, heat transport feature enhances for the augmentation in the Eckert number which is exhibited for the inclusion of dissipative heat.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100993"},"PeriodicalIF":0.0,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698702","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

Analytical solutions for autonomous differential equations with weighted derivatives 带加权导数的自主微分方程的解析解

Partial Differential Equations in Applied Mathematics Pub Date : 2024-11-10 DOI: 10.1016/j.padiff.2024.100980

Rami AlAhmad , Mohammad Al-Khaleel

引用次数: 0

An analytical investigation of the Van Der Waals gas system: Dynamics insights into bifurcation, optical pattern along with sensitivity and chaotic analysis 范德瓦耳斯气体系统分析研究：对分岔、光学模式以及敏感性和混沌分析的动力学见解

Partial Differential Equations in Applied Mathematics Pub Date : 2024-11-09 DOI: 10.1016/j.padiff.2024.100983

Muhammad Moneeb Tariq , Muhammad Aziz-ur-Rehman , Muhammad Bilal Riaz

{"title":"An analytical investigation of the Van Der Waals gas system: Dynamics insights into bifurcation, optical pattern along with sensitivity and chaotic analysis","authors":"Muhammad Moneeb Tariq , Muhammad Aziz-ur-Rehman , Muhammad Bilal Riaz","doi":"10.1016/j.padiff.2024.100983","DOIUrl":"10.1016/j.padiff.2024.100983","url":null,"abstract":"<div><div>This paper focuses on obtaining exact solutions for the nonlinear Van der Waals gas system using the modified Khater method. Renowned as one of the latest and most precise analytical schemes for nonlinear evolution equations, this method has proven its efficacy by generating diverse solutions for the model under consideration. The governing equation is transformed into an ordinary differential equation through a well-suited wave transformation. This analytical simplification makes it possible to use the provided methods to derive trigonometric, rational, and hyperbolic solutions. To illuminate the physical behavior of the model, graphical plots of selected solutions are presented. By selecting appropriate values for arbitrary factors, this visual representation enhances comprehension of the dynamical system. Furthermore, the system undergoes a certain transformation to become a planar dynamical system, and the bifurcation analysis is examined. Additionally, the sensitivity analysis of the dynamical system is conducted using the Runge–Kutta method to confirm that slight alterations in the initial conditions have minimal impact on the stability of the solution. The presence of chaotic dynamics in the Van der Waals gas system is explored by introducing a perturbed term in the dynamical system. Two and three-dimensional phase profiles are used to illustrate these chaotic behaviors.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100983"},"PeriodicalIF":0.0,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652675","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

Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience 研究神经科学课题中出现的时空分数孤子神经元模型方程的波谱参数效应

Partial Differential Equations in Applied Mathematics Pub Date : 2024-11-09 DOI: 10.1016/j.padiff.2024.100985

Md. Nur Alam, Md. Azizur Rahman

{"title":"Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience","authors":"Md. Nur Alam, Md. Azizur Rahman","doi":"10.1016/j.padiff.2024.100985","DOIUrl":"10.1016/j.padiff.2024.100985","url":null,"abstract":"<div><div>Time-space fractional nonlinear problems (T-SFNLPs) play a crucial role in the study of nonlinear wave propagation. Time-space nonlinearity is prevalent across various fields of applied science, nonlinear dynamics, mathematical physics, and engineering, including biosciences, neurosciences, plasma physics, geochemistry, and fluid mechanics. In this context, we examine the time-space fractional soliton neuron model (TSFSNM), which holds significant importance in neuroscience. This model explains how action potentials are initiated and propagated by axons, based on a thermodynamic theory of nerve pulse transmission. The signals passing through the cell membrane (CM) are proposed to take the form of solitary sound pulses, which can be represented as solitons. To investigate these soliton solutions, nonlinear fractional differential equations (NLFDEs) are transformed into corresponding partial differential equations (PDEs) using a fractional complex transform (FCT). The Kudryashov method is then applied to determine the wave profiles for the TSFSNM equation. We present 3D, 2D, contour, and density plots of the TSFSNM equation, and further analyze how fractional and time-space parameters influence these wave profiles through additional graphical representations. Kink, singular kink and different types of soliton solutions are successfully recovered through the Kudryashov method. The outcomes of various studies show that the applied method is highly efficient and well-suited for tackling problems in applied sciences and mathematical physics. Graphical representations, coupled with numerical data, reinforce the validity and accuracy of the technique. The proposed method is a convenient and powerful tool for handling the solution of nonlinear equations, making it particularly effective in exploring complex wave phenomena in diverse scientific fields.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100985"},"PeriodicalIF":0.0,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652681","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

Exact solution to a class of problems for the Burgers’ equation on bounded intervals 有界区间上布尔格斯方程一类问题的精确解

Partial Differential Equations in Applied Mathematics Pub Date : 2024-11-09 DOI: 10.1016/j.padiff.2024.100977

Kwassi Anani , Mensah Folly-Gbetoula

{"title":"Exact solution to a class of problems for the Burgers’ equation on bounded intervals","authors":"Kwassi Anani , Mensah Folly-Gbetoula","doi":"10.1016/j.padiff.2024.100977","DOIUrl":"10.1016/j.padiff.2024.100977","url":null,"abstract":"<div><div>In this study, we consider Burgers’ equation with fixed Dirichlet boundary conditions on generic bounded intervals. By employing the Hopf–Cole transformation and a recently established exact operational solution for linear reaction–diffusion equations, an exact solution in the time domain is derived through inverse Laplace transforms. In the event that analytic inverses do in fact exist, they can be obtained in closed form through the use of Mellin transforms. Nevertheless, highly efficient algorithms are available, and numerical inverses in the time domain are always feasible, regardless of the complexity of the Laplace domain expressions. Two illustrative tests demonstrate that the results align closely with those of classical exact solutions. In comparison to the solutions obtained with series expressions or by numerical methods, closed-form expressions, even in the Laplace domain, represent a novel alternative, offering new insights and perspectives. The exact solution via the inverse Laplace transform is shown to be more computationally efficient, providing a reference point for numerical and semi-analytical methods.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100977"},"PeriodicalIF":0.0,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652676","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

Computational study of time-fractional non-linear Kawahara equations using Quintic B-spline and Galerkin’s method 使用 Quintic B-样条和 Galerkin 方法对时间分数非线性川原方程的计算研究

Partial Differential Equations in Applied Mathematics Pub Date : 2024-11-06 DOI: 10.1016/j.padiff.2024.100779

Shams Ul Arifeen , Ihteram Ali , Imtiaz Ahmad , Sadaf Shaheen

引用次数: 0