Partial Differential Equations in Applied Mathematics最新文献

英文中文

Exploring the dynamics of leprosy transmission with treatment through a fractal–fractional differential model 通过分形-分数微分模型探索麻风病传播与治疗的动态关系

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-16 DOI: 10.1016/j.padiff.2024.100909

Khadija Tul Kubra , Rooh Ali , Bushra Ujala , Samra Gulshan , Tayyaba Rasool , Mohamed Reda Ali

Leprosy continues to be a significant public health challenge in many parts of the world, necessitating novel approaches to understanding and controlling its transmission. The dynamics of leprosy are examined in this study by means of a caputo fabrizio fractal–fractional differential system model. Leprosy transmission and treatment are complex and non-linear processes that can be captured by fractal–fractional derivatives. The temporal progression of the disease is the primary focus of our mathematical analysis, which evaluates a variety of parameter values, including initial population densities and compartmental transitions. Through simulations, we examine the impact of critical parameters on the severity and spread of diseases, as well as the rates of recovery and treatment. Numerical results of the model offer valuable insights into the impact of these parameters on leprosy dynamics, which is beneficial for public health interventions. The stability analysis of the model identifies supplementary conditions that are necessary for the success of disease control. By incorporating these novel mathematical techniques, we hope to improve our understanding of leprosy transmission and ultimately contribute to more effective control strategies. Based on our findings, additional studies investigating the relation between population density, treatment accessibility, and recovery rates are warranted. We hope that by graphically representing the relationships between these factors, we can draw attention to the possibility of targeted interventions that can reduce the transmission of leprosy. This study provides a strong basis for future studies on infectious disease modeling and aids leprosy-affected communities in developing strategies to mitigate the disease’s impact.

麻风病在世界许多地区仍然是一项重大的公共卫生挑战，因此需要采用新的方法来了解和控制其传播。本研究通过一个 caputo fabrizio 分形-分数微分系统模型对麻风病的动态过程进行了研究。麻风病的传播和治疗是复杂的非线性过程，可以用分形-分数导数来捕捉。疾病的时间进展是我们数学分析的主要重点，我们评估了各种参数值，包括初始人口密度和区隔转换。通过模拟，我们研究了关键参数对疾病严重程度和传播以及康复率和治疗率的影响。模型的数值结果为了解这些参数对麻风病动态的影响提供了有价值的见解，有利于公共卫生干预。模型的稳定性分析确定了成功控制疾病的必要补充条件。通过采用这些新颖的数学技术，我们希望能加深对麻风病传播的理解，并最终为制定更有效的控制策略做出贡献。基于我们的研究结果，有必要对人口密度、治疗可及性和康复率之间的关系进行更多研究。我们希望通过图解这些因素之间的关系，能够引起人们的注意，从而采取有针对性的干预措施，减少麻风病的传播。这项研究为今后的传染病模型研究奠定了坚实的基础，并有助于麻风病社区制定减轻麻风病影响的策略。

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引用次数: 0

Entwining tetrahedron maps 缠绕四面体图

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-15 DOI: 10.1016/j.padiff.2024.100949

Pavlos Kassotakis

We present three non-equivalent procedures to obtain entwining (non-constant) tetrahedron maps. Given a tetrahedron map, the first procedure incorporates its underlying symmetry group. With the second procedure we obtain several classes of entwining tetrahedron maps by considering certain compositions of pentagon with reverse-pentagon maps which satisfy certain compatibility relations the so-called ten-term relations. Using the third procedure, provided that a given tetrahedron map admits at least one companion map (partial inverse), we obtain entwining set theoretical solutions of the tetrahedron equation.

我们提出了三种非等价程序来获得缠绕（非恒定）四面体映射。给定一个四面体映射，第一种程序包含其基本对称群。利用第二种程序，我们通过考虑五边形与反五边形映射的某些组合，得到了几类缠绕四面体映射，这些组合满足某些相容性关系，即所谓的十项关系。利用第三种程序，只要给定的四面体映射允许至少一个伴映射（部分逆映射），我们就能得到四面体方程的缠绕集理论解。

引用次数: 0

Tensor product solutions of certain Abstract Cauchy problems of Euler type 某些欧拉型抽象考奇问题的张量积解

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-15 DOI: 10.1016/j.padiff.2024.100957

Sharifa Al-Sharif , Batool Momani , Jamila Jawdat

Our concern in this paper, is to find exact solutions, using tensor product techniques, of two types of second order homogeneous Abstract Cauchy problems of the following forms

u^{″} (t) + C u^{'} (t) + F u (t) = 0,

and

t^{2} u^{''} (t) + 2 t C u^{'} (t) + F u (t) = 0 .

The initial conditions to be used are

u (t_{0}) = u_{0}, u^{'} (t_{0}) = u_{0}^{'},

where

C

and

F

are closed linear operators that are densely defined on a Banach space

Y

u_{0}, u_{0}^{'} \in Y

and

u \in C^{2} (I, Y) .

本文关注的是利用张量乘积技术找到以下两种形式的二阶均质抽象考基问题的精确解：u″(t)+Cu′(t)+Fu(t)=0 和 t2u′′(t)+2tCu′(t)+Fu(t)=0。使用的初始条件为 u(t0)=u0,u′(t0)=u0′，其中 C 和 F 是密定义在巴纳赫空间 Y 上的封闭线性算子，u0,u0′∈Y 和 u∈C2(I,Y)。

引用次数: 0

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

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-15 DOI: 10.1016/j.padiff.2024.100955

M.A. El-Shorbagy , Sonia Akram , Mati ur Rahman

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

(2 + 1)

-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.

在当前的研究中，我们利用新扩展直接代数法（NEDAM）和符号计算法，以及不同的测试函数和 Hirota 双线性方法，来确保 (2+1)-dimensional 分数电信系统的孤子和块解。因此，我们得出了具有复杂结构的孤子解，如混合三角函数解、有理函数解、双曲线解、唯一解、周期解、暗-亮解、亮-暗解和双曲线解。我们还开发了一种包含流氓波和呼吸器的块状解，以满足好奇心的智力需求。这些特征对于控制光通信中的极端现象非常重要。此外，我们还研究了非线性光纤的调制不稳定性（MI）。了解调制不稳定性对于开发可利用其积极特性或减轻其不利影响的系统至关重要。此外，我们还对观测到的模型进行了全面的敏感性分析，以评估不同因素的影响。在计算机应用程序的帮助下，结果的三维表面和二维视觉效果、等值线和密度图都得到了体现。我们的研究结果证明了利用孤子理论和先进的非线性分析方法提高电信系统性能的潜力。

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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

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-14 DOI: 10.1016/j.padiff.2024.100953

Anjali , Seema Mehra , Renu Chugh , Dania Santina , Nabil Mlaiki

Throughout this study, we present a new algorithm for finding the common solution of a finite family of monotone inclusion and the fixed point problem of a finite family of generalized demimetric operators in the context of a real Hilbert space and show its strong convergence. Moreover, we utilize our result to solve the minimization problem.

在本研究中，我们提出了一种新算法，用于在实希尔伯特空间的背景下寻找有限单调包含族的公共解和有限广义非计量算子族的定点问题，并证明了其强大的收敛性。此外，我们还利用我们的结果解决了最小化问题。

引用次数: 0

Three-dimensional stagnation point motion of bioconvection nanofluid via moving stretching sheet with convective and anisotropic slip condition 具有对流和各向异性滑移条件的生物对流纳米流体通过移动拉伸片的三维停滞点运动

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-12 DOI: 10.1016/j.padiff.2024.100958

Nune Pratyusha , Nainaru Tarakaramu , Suresh Babu R , V.K. Somasekhar Srinivas , Furqan Ahmad , M. Waqas , Barno Abdullaeva , Manish Gupta

The current article deals with the SM of a NFs on a 3D moving surface containing bioconvection, microorganisms, and convective conditions over anisotropic slip. This work reports describes the characteristics of bioconvection aspects of nanofluid containing microorganisms with anisotropic slip condition. The study may be important from the application point of view in microfluidic devices, antibiotics, enhanced oil recovery and many other areas. Applying the similarity variables, the basic gov. Eqs are translated to ordinary ones, and such Eqs are calculate by R-K-F fourth order programming with shooting scheme by MATLAB software. The physical parameters on the moving surface are explained in detail via graphs. We found that the temperature increases with a higher revolution and larger numerical numbers (convection parameter), while the HTR declined for various values of the SFP. The HTR enhances with surface convection, and therefore, the convection condition is helpful in reducing the viscous drag on the moving SS.

本文探讨了三维运动表面上的纳米流体的生物对流、微生物和各向异性滑移条件下的对流条件。这项研究描述了各向异性滑移条件下含微生物纳米流体的生物对流特性。从微流体设备、抗生素、提高石油采收率和许多其他领域的应用角度来看，这项研究可能具有重要意义。应用相似性变量，基本 gov.利用相似性变量，将基本工程方程转化为普通方程，并通过 MATLAB 软件的 R-K-F 四阶程序和射影方案计算这些方程。通过图表详细解释了运动表面的物理参数。我们发现，温度随着转速的升高和数值（对流参数）的增大而升高，而 HTR 则随着 SFP 的不同值而下降。HTR 随表面对流而增强，因此，对流条件有助于减少运动 SS 上的粘性阻力。

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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

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-11 DOI: 10.1016/j.padiff.2024.100950

Muayyad Mahmood Khalil , Siddiq Ur Rehman , Ali Hasan Ali , Rashid Nawaz , Belal Batiha

This manuscript presents enhanced versions of two methods: the natural transform iterative method (NTIM) and the q-homotopy analysis method (q-HAM). These methods harness concepts from Fractional Calculus, particularly leveraging the Caputo fractional derivative operator, to successfully manage the complexities of fractional-order systems. To validate their accuracy and efficiency, we applied the proposed techniques to FPDEs like the fractional-order KDV-Burger and fifth-order Sawada–Kotera equations. Our outcomes, which closely resemble the exact solutions, demonstrate how useful NTIM and q-HAM are for solving difficult FPDEs and improving the study of fractional calculus.

本手稿介绍了两种方法的增强版本：自然变换迭代法（NTIM）和 q-同调分析法（q-HAM）。这些方法利用分数微积分的概念，特别是利用卡普托分数导数算子，成功地处理了分数阶系统的复杂性。为了验证其准确性和效率，我们将所提出的技术应用于分数阶 KDV-Burger 和五阶 Sawada-Kotera 方程等 FPDE。我们的结果与精确解非常相似，这表明 NTIM 和 q-HAM 对于解决困难的 FPDE 和改进分数微积分研究非常有用。

引用次数: 0

Anisotropic error estimator for the Stokes–Biot system 斯托克斯-比奥系统的各向异性误差估计器

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-11 DOI: 10.1016/j.padiff.2024.100952

Houédanou Koffi Wilfrid

This paper presents an a posteriori error analysis for the problem defining the interaction between a free fluid and poroelastic structure approximated by finite element methods on anisotropic meshes in

R^{d}

d = 2

or 3. Korn’s inequality for piecewise linear vector fields on anisotropic meshes is established and is applied to nonconforming finite element method. Then the existence and uniqueness of the approximation solution are deduced for conforming and nonconforming cases. With the obtained finite element solutions, local error indicators and a global estimator are generated, demonstrating reliability and efficiency. The efficiency is proved by means of bubble functions and the corresponding anisotropic inverse inequalities. In order to prove the reliability, it is vital that an anisotropic mesh corresponds to the anisotropic function under consideration. To measure this correspondence, a so-called matching function is defined, and its discussion shows it to be useful tool. With its help, the upper error bound is shown by means of the corresponding anisotropic interpolation estimates and a special Helmholtz decomposition in both media.

本文对自由流体与孔弹性结构之间的相互作用问题进行了后验误差分析，该问题用各向异性网格（d=2 或 3）上的有限元方法进行近似。建立了各向异性网格上片断线性矢量场的 Korn 不等式，并将其应用于非符合有限元法。然后推导出符合和不符合情况下近似解的存在性和唯一性。利用所获得的有限元解，生成局部误差指标和全局估算器，证明了其可靠性和高效性。通过气泡函数和相应的各向异性反不等式证明了效率。为了证明可靠性，各向异性网格必须与所考虑的各向异性函数相对应。为了衡量这种对应关系，定义了一个所谓的匹配函数，对它的讨论表明它是一个有用的工具。在它的帮助下，通过相应的各向异性插值估计和两种介质中的特殊亥姆霍兹分解，显示了误差上限。

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引用次数: 0

A study on the fractional-order COVID-19 SEIQR model and parameter analysis using homotopy perturbation method 分数阶 COVID-19 SEIQR 模型研究及同调扰动法参数分析

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-10 DOI: 10.1016/j.padiff.2024.100960

Mominul Islam, M. Ali Akbar

In this article, we present a fractional-order susceptible-exposed-infected-quarantine-recovered (SEIQR) model to analyze the dynamics of the COVID-19 pandemic. The model includes susceptible (S), exposed (E), infected (I), quarantined (Q), and recovered (R) populations and uses a fractional-order differential equation to provide a further accurate representation of the disease's progression. We employ the homotopy perturbation method (HPM) to derive analytical solutions and the Runge-Kutta fourth-order (RK4) method to obtain numerical solutions. The results indicate that the fractional-order model, particularly for a fractional parameter α = 0.40, provides better accuracy and stability compared to the classical integer-order model. This study highlights the importance of fractional-order modeling in understanding the spread of COVID-19 and suggests its potential application in predicting and controlling future epidemics.

在本文中，我们提出了一个分数阶易感-暴露-感染-隔离-恢复（SEIQR）模型来分析 COVID-19 大流行的动态。该模型包括易感人群（S）、暴露人群（E）、感染人群（I）、检疫人群（Q）和康复人群（R），并使用分数阶微分方程来进一步精确表示疾病的发展过程。我们采用同调扰动法（HPM）得出解析解，并采用 Runge-Kutta 四阶法（RK4）获得数值解。结果表明，与经典整数阶模型相比，分数阶模型，尤其是分数参数 α = 0.40 时，具有更好的精度和稳定性。这项研究强调了分数阶模型在理解 COVID-19 传播方面的重要性，并提出了其在预测和控制未来流行病方面的潜在应用。

引用次数: 0

Innovative approache for the nonlinear atangana conformable Klein-Gordon equation unveiling traveling wave patterns 揭示行波模式的非线性阿坦加纳共形克莱因-戈登方程创新方法

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-10 DOI: 10.1016/j.padiff.2024.100935

Hadi Rezazadeh , Mohammad Ali Hosseinzadeh , Lahib Ibrahim Zaidan , Fatima SD. Awad , Fiza Batool , Soheil Salahshour

The aim of current work is to establish novel traveling wave solutions of the nonlinear Atangana conformable Klein - Gordon equation using a new extended direct algebraic technique. The Klein - Gordon equation is the relativistic state of the Schrödinger equation with a second - order time derivative and zero spin. Complex wave variable transformation is used to convert Atangana conformable nonlinear differential equation into an ordinary differential equation. Using the proposed technique based on Maple software structure, various types of solutions, such as, generalized trigonometric, generalized hyperbolic, and exponential functions, are established. When special parameteric values are considered for this method, solitary wave solutions can be obtained through other methods, such as the (

\frac{G^{'}}{G}

)-expansion method, the modified Kudryashov method, the sub-equation method, and so forth. A physical explanation is provided for the solutions under consideration to enhance comprehension of the physical phenomena resulting from the obtained solutions, provided that the physical parameters are set appropriately using 3D, 2D, and contour simulations. The results demonstrated that the new extended direct algebraic method provides a more potent mathematical tool for solving numerous more nonlinear partial differential equations with the aid of symbolic computation.

当前工作的目的是利用一种新的扩展直接代数技术，建立非线性阿坦加纳共形克莱因-戈登方程的新型行波解。克莱因-戈登方程是具有二阶时间导数和零自旋的薛定谔方程的相对论状态。复波变量变换用于将阿坦加纳符合非线性微分方程转换为常微分方程。利用基于 Maple 软件结构的拟议技术，建立了各种类型的解，如广义三角函数、广义双曲函数和指数函数。当考虑到该方法的特殊参数值时，孤波解可通过其他方法获得，如（G′G）展开法、修正库德里亚肖夫法、子方程法等。在利用三维、二维和等值线模拟对物理参数进行适当设置的前提下，为所考虑的解提供了物理解释，以加深对所获解产生的物理现象的理解。结果表明，新的扩展直接代数方法为借助符号计算求解更多的非线性偏微分方程提供了更有力的数学工具。

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