Partial Differential Equations in Applied Mathematics最新文献

英文中文

Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method 利用阿坦加纳-巴莱亚努-卡普托分数导数与定点法计算尼帕病毒模型的海尔-乌兰稳定性

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-27 DOI: 10.1016/j.padiff.2024.100939

In this study, we present a novel investigation into the dynamics of the Nipah virus through the lens of fractional differential equations (FDEs), employing the Atangana–Baleanu–Caputo fractional derivative (ABCFD) and the fixed-point approach (FPA). The core contribution of this work lies in establishing the existence and uniqueness of solutions to the proposed FDEs, a critical step for validating the model. Furthermore, we explore the Hyers–Ulam (HU) stability of these generalized FDEs, providing a rigorous mathematical foundation for the stability analysis within the context of viral dynamics. By leveraging the ABCFD, our work extends the classical stability criteria, offering new insights into the role of memory effects in disease modeling. Additionally, we present approximate solutions across various compartments and fractional orders, highlighting the sensitivity of the system to key parameters. Numerical simulations, conducted using the Cullis method, illustrate the impact of fractional orders and validate the theoretical findings, positioning this work as a significant advancement in the application of fractional calculus to epidemiological models.

在本研究中，我们采用阿坦加纳-巴莱亚努-卡普托分数导数 (ABCFD) 和定点法 (FPA)，通过分数微分方程 (FDE) 的视角对尼帕病毒的动态进行了新颖的研究。这项工作的核心贡献在于建立了拟议 FDE 的解的存在性和唯一性，这是验证模型的关键步骤。此外，我们还探索了这些广义 FDE 的海尔-乌兰（HU）稳定性，为病毒动力学背景下的稳定性分析提供了严格的数学基础。通过利用 ABCFD，我们的工作扩展了经典稳定性标准，为疾病建模中记忆效应的作用提供了新的见解。此外，我们还提出了各种区间和分数阶的近似解，突出了系统对关键参数的敏感性。使用 Cullis 方法进行的数值模拟说明了分数阶数的影响，并验证了理论发现，使这项工作成为将分数微积分应用于流行病学模型的重大进展。

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引用次数: 0

Dynamical behavior of tempered φ-Caputo type fractional order stochastic differential equations driven by Lévy noise 莱维噪声驱动的回火φ-卡普托型分数阶随机微分方程的动力学行为

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-27 DOI: 10.1016/j.padiff.2024.100938

This paper focuses on the analysis of a class of stochastic differential equations with tempered

φ

-Caputo fractional derivative (

φ

-CFD) and Lévy noise. We propose comprehensive mathematical techniques to address the existence, uniqueness and stability of solution to this equation. For existence and uniqueness, the Picard–Lindelof successive approximation technique is used analyze the results. Also, We use Mittag-Leffler (M-L) function to investigate the stability of the solution. This research applies the broad understanding of stochastic processes and fractional differential equations, as well as known results, to the analysis of systems with tempered

φ

-CFD. These equations capture complex phenomena in the field of financial assets, making their investigation on the stock prices particularly valuable.

本文重点分析一类具有调和φ-卡普托分数导数（φ-CFD）和莱维噪声的随机微分方程。我们提出了综合数学技术来解决该方程解的存在性、唯一性和稳定性问题。对于存在性和唯一性，我们采用了 Picard-Lindelof 逐次逼近技术来分析结果。此外，我们还使用 Mittag-Leffler (M-L) 函数来研究解的稳定性。这项研究将对随机过程和分式微分方程的广泛理解以及已知结果应用于分析有节制的 φ-CFD 系统。这些方程捕捉了金融资产领域的复杂现象，因此对股票价格的研究尤为重要。

引用次数: 0

Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity 在无穷远处具有简单行为的非线性延迟微分方程系统的动力学特性

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-26 DOI: 10.1016/j.padiff.2024.100934

In this paper, we study the dynamics of a system of nonlinear differential equations with delay. We find stable equilibrium states and regions of attraction to them in the phase space of the system, as well as stable and unstable homogeneous and inhomogeneous cycles. We find conditions on the parameters of the system for multistability. We show that the coupling parameter has a decisive influence on the dynamics of the system. We find regions of the parameters of the system and extensive sets of initial conditions such that if we take these values of the parameters and any initial conditions from these sets, the system will have simple dynamics.

在本文中，我们研究了一个带延迟的非线性微分方程系统的动力学。我们在系统的相空间中找到了稳定的平衡态和吸引平衡态的区域，以及稳定和不稳定的同质和非同质循环。我们找到了系统多稳定性的参数条件。我们证明了耦合参数对系统动力学的决定性影响。我们找到了系统参数的区域和初始条件的广泛集合，如果我们从这些集合中提取这些参数值和任何初始条件，系统将具有简单的动力学特性。

引用次数: 0

Mathematical analysis of soliton solutions in space-time fractional Klein-Gordon model with generalized exponential rational function method 用广义指数有理函数法对时空分数克莱因-戈登模型中的孤子解进行数学分析

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-25 DOI: 10.1016/j.padiff.2024.100942

In this article, we investigate the space-time Klein-Gordon (KG) model, a significant framework in quantum field theory and quantum mechanics, which also describes phenomena such as wave propagation in crystal dislocations. This model is particularly important in high-energy particle physics. The novelty of this article is to examine the sufficient, useful in optical fibers, and further general soliton solutions of the nonlinear KG model using the generalized exponential rational function method (GERFM), which do not exist in the recent literature. The fractional complex wave transformation is utilized to turn the model into a nonlinear form, and the accuracy of the acquired solutions is confirmed by reintroducing them into the original models using Mathematica. The obtained solutions are expressed in hyperbolic, exponential, rational, and trigonometric forms. We elucidate the fractional effects for specific parameter values, accompanied by illustrative figures. Our results demonstrate that GERFM is effective, powerful, and versatile, providing exact traveling wave solutions for various nonlinear models in engineering and mathematical physics. Our findings reveal that the characteristics of soliton-shaped waves in both three-dimensional and two-dimensional contexts are profoundly influenced by fractional order derivative. This study advances the understanding of nonlinear wave dynamics and offers a robust method for solving complex physical models.

在这篇文章中，我们研究了时空克莱因-戈登（KG）模型，它是量子场论和量子力学的一个重要框架，也描述了晶体位错中的波传播等现象。该模型在高能粒子物理学中尤为重要。本文的新颖之处在于利用广义指数有理函数法（GERFM）研究了非线性 KG 模型的充分解、光纤中的有用解以及进一步的一般孤子解，而这些解在最近的文献中并不存在。利用分数复波变换将模型转化为非线性形式，并通过使用 Mathematica 将获得的解重新引入原始模型来确认其准确性。获得的解以双曲、指数、有理和三角形式表示。我们阐明了特定参数值的分数效应，并附有说明性数字。我们的研究结果表明，GERFM 有效、强大且用途广泛，能为工程和数学物理中的各种非线性模型提供精确的行波解。我们的研究结果表明，孤子形波在三维和二维环境中的特性深受分数阶导数的影响。这项研究加深了人们对非线性波动力学的理解，并为复杂物理模型的求解提供了一种稳健的方法。

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引用次数: 0

Nonlinear dynamics model of HIV/AIDS: Assessing the impacts of condoms, vaginal microbicides, and optimized treatment 艾滋病毒/艾滋病非线性动力学模型：评估安全套、阴道杀菌剂和优化治疗的影响

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-25 DOI: 10.1016/j.padiff.2024.100933

HIV/AIDS remains one of the main global causes of morbidity and mortality. While antiretroviral drugs are still the only treatment for HIV patients, their accessibility and efficient delivery in resource-poor nations constitute a major concern, and no epidemiological model has considered this. Based on this, we create a model for HIV/AIDS that considers condoms and vaginal microbicides alongside saturated treatment. We consider the constant control case, in which theoretical results show that the delay factor in the antiretroviral therapy (ART) regimen can induce backward bifurcation, which consequently distorts the global effort to end HIV incidence. We use the Castillo-Chavez stability to ensure that the disease-free equilibrium is globally asymptotically stable whenever the associated reproduction number is less than one. Uncertainty and sensitivity analysis using the Latin hypercube sampling technique was also carried out on the parameters and state variables of the model equations, and the result shows that half of the most highly influential parameters are capable of reducing cases of HIV and AIDS. For time-dependent control cases, our findings suggest that, in countries with low income, directing resources to either condom use or vaginal microbicides is more effective than a regular intake of antiretrovirals alone. Furthermore, results without ART delay have shown to be more effective in HIV control than others where the inaccessibility of the therapy encouraged outbursts of AIDS cases. Thus, as reliable as antiretrovirals are in HIV/AIDS treatment, early administration and regular intake are key to their continued success.

艾滋病毒/艾滋病仍然是全球发病和死亡的主要原因之一。虽然抗逆转录病毒药物仍然是治疗艾滋病患者的唯一方法，但在资源匮乏的国家，这些药物的可及性和有效供应是一个令人担忧的主要问题，目前还没有任何流行病学模型考虑到这一点。在此基础上，我们创建了一个艾滋病毒/艾滋病模型，该模型在考虑饱和治疗的同时，还考虑了安全套和阴道杀菌剂。我们考虑了恒定控制的情况，理论结果表明，抗逆转录病毒疗法（ART）方案中的延迟因素会诱发后向分叉，从而扭曲全球消除艾滋病发病率的努力。我们使用卡斯蒂略-查韦斯稳定性来确保无病平衡在相关繁殖数小于 1 时是全局渐近稳定的。我们还利用拉丁超立方采样技术对模型方程的参数和状态变量进行了不确定性和敏感性分析，结果表明，影响最大的参数中有一半能够减少艾滋病毒和艾滋病病例。对于与时间相关的控制病例，我们的研究结果表明，在低收入国家，将资源用于使用安全套或阴道杀菌剂比单独定期服用抗逆转录病毒药物更有效。此外，在抗逆转录病毒疗法没有延迟的情况下，与其他因无法获得治疗而导致艾滋病病例爆发的国家相比，抗逆转录病毒疗法的效果更佳。因此，尽管抗逆转录病毒药物在艾滋病毒/艾滋病治疗中是可靠的，但及早用药和定期服药是其持续成功的关键。

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引用次数: 0

Computational precision in time fractional PDEs: Euler wavelets and novel numerical techniques 时间分数 PDE 的计算精度：欧拉小波和新型数值技术

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-24 DOI: 10.1016/j.padiff.2024.100918

This paper presents innovative numerical methodologies designed to solve challenging time fractional partial differential equations, with a focus on the Burgers’, Fisher–KPP, and nonlinear Schrödinger equations. By employing advanced wavelet techniques integrated with fractional calculus, we achieve highly accurate solutions, surpassing conventional methods with minimal absolute error in numerical simulations. A thorough series of numerical experiments validates the robustness and effectiveness of our approach across various parameter regimes and initial conditions. The results underscore significant advancements in the computational modeling of complex physical phenomena governed by time fractional dynamics and offering a powerful tool for a wide range of applications in science and engineering.

本文介绍了旨在求解具有挑战性的时间分数偏微分方程的创新数值方法，重点是布尔格斯方程、费希尔-KPP方程和非线性薛定谔方程。通过采用与分数微积分相结合的先进小波技术，我们实现了高精度求解，在数值模拟中以最小的绝对误差超越了传统方法。一系列全面的数值实验验证了我们的方法在各种参数机制和初始条件下的稳健性和有效性。这些结果突显了时间分数动力学在复杂物理现象计算建模方面取得的重大进展，为科学和工程领域的广泛应用提供了强有力的工具。

引用次数: 0

Entropy analysis in magnetized blood-based hybrid nanofluid flow via parallel disks 磁化血液混合纳米流体流经平行盘的熵分析

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-24 DOI: 10.1016/j.padiff.2024.100941

Magnetized hybrid nanofluid combined with ferrite and silver in a blood-based liquid presents their vital role in several aspects such as artificial heart pumping system, drug delivery process, the flow of blood in the artery, etc. This is because the high heat transportation rate of the nanofluid is caused by the inclusion of nanoparticles. The current investigation is based on the characteristic of particle concentration comprised of Fe₃O₄ and Ag in the base liquid blood that passed in between two infinite parallel disks filled with porous matrix. The electrically conducting fluid associated to maximum of 1.5 % of volume concentration from each of the solid particles affects the flow phenomena. However, the impact of thermal radiation vis-à-vis the heat dissipation provides efficient heat transport properties with the inclusion of the effective thermal conductivity assumed from the Hamilton-Crosser model. The proposed conductivity model describes the role of particle shapes on the enhanced thermal properties. Further, numerical treatment is obtained for the transformed designed problem following similarity rules that are used for the conversion of the governing equations into their non-dimensional form. The computation of various flow profiles leads to get the entropy generation due to the irreversibility processes. Along with the fluid velocity and temperature distributions, the study is carried out for the entropy as well as the computation of Bejan number and afterwards the simulation of the shear and heat transportation rate are also depicted graphically. The main finding of the proposed study is that solid particle concentrations have a substantial impact to increasing fluid velocity in magnitude, resulting in a narrower wall thickness at both channel walls. Thermal radiation was shown to be more effective at increasing entropy generation and Bejan value.

在血液基液体中加入铁氧体和银的磁化混合纳米流体在人工心脏泵送系统、药物输送过程、动脉血流等多个方面发挥了重要作用。这是因为纳米粒子的加入导致了纳米流体的高热传输率。目前的研究基于在两个充满多孔基质的无限平行圆盘之间流动的血液基液中由 Fe3O4 和 Ag 组成的颗粒浓度特征。每种固体颗粒体积浓度最大为 1.5% 的导电流体会影响流动现象。然而，热辐射对散热的影响通过加入汉密尔顿-克罗斯模型假定的有效热传导率提供了有效的热传输特性。所提出的导热模型描述了颗粒形状对增强热特性的作用。此外，还根据相似性规则对转化后的设计问题进行了数值处理，这些规则用于将控制方程转换为非维度形式。通过对各种流动剖面的计算，可以得到由于不可逆过程而产生的熵。在研究流体速度和温度分布的同时，还研究了熵和贝扬数的计算，之后还以图形方式描述了剪切力和热传输率的模拟。拟议研究的主要发现是，固体颗粒浓度对增加流体速度的幅度有很大影响，导致两个通道壁的壁厚变窄。热辐射在增加熵生成和贝扬值方面更为有效。

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引用次数: 0

Numerical illustration using finite difference method for the transient flow through porous microchannel and statistical interpretation of entropy using response surface methodology 利用有限差分法对多孔微通道中的瞬态流动进行数值说明，并利用响应面方法对熵进行统计解释

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-24 DOI: 10.1016/j.padiff.2024.100940

The current article discloses the influence of the hyperbolic tangent nanofluid on time dependent flow through a microchannel when a magnetic field is applied. The porous medium was incorporated using the Darcy–Forchheimer model. The chemical reaction is explained by Arrhenius activation energy. Temperature is determined by convective boundary conditions. The irreversibility occurring in the flow is analyzed. The modeled problem gives rise to partial differential equations, which are computed by finite difference method. Response surface methodology, an optimization technique, is used to attain the optimal conditions for entropy generated for the flow of fluid. Results of the analysis reveal that concentration decreases with the rise in reaction rate parameter and increases with activation energy parameter. Prandtl and Eckert numbers, with their increase, enhance entropy, and fluid friction irreversibility is at its highest. Perfect co-relation is attained for the model by the response surface methodology, with a co-relation coefficient of 100 %. The Weissenberg number is highly sensitive to change in the present modeling, followed by Darcy and Reynolds numbers. The Reynolds number and Darcy number show positive sensitivity, while the Weissenberg number shows negative sensitivity to the entropy generated.

本文介绍了双曲切线纳米流体在施加磁场时对微通道中随时间变化的流动的影响。采用达西-福克海默（Darcy-Forchheimer）模型纳入了多孔介质。化学反应由阿伦尼乌斯活化能解释。温度由对流边界条件决定。对流动中出现的不可逆现象进行了分析。建模问题产生了偏微分方程，并通过有限差分法进行计算。响应面法是一种优化技术，用于获得流体流动产生熵的最佳条件。分析结果表明，浓度随反应速率参数的增加而降低，随活化能参数的增加而升高。随着普朗特数和埃克特数的增加，熵增大，流体摩擦不可逆性达到最高。通过响应面方法，模型达到了完美的相关性，相关系数为 100%。在本模型中，魏森堡数对变化高度敏感，其次是达西数和雷诺数。雷诺数和达西数显示出正敏感性，而魏森伯格数对所产生的熵显示出负敏感性。

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引用次数: 0

Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI method 通过 AFVI 方法分析某些分数非线性演化方程的近似解

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-23 DOI: 10.1016/j.padiff.2024.100937

In this article, we construct and investigate a new fractional variational iteration technique which is named as AFVI method. After that, we formulate some IVPs corresponding to the fractional nonlinear evolution equations NLTFFWE, mNLTFFWE, TFmCHE and TFmDPE. The Caputo fractional order derivative has been used to fractionalize the considered NLEEs. Then, we solve the considered IVPs by applying the formulated AFVI method. Lastly, we check the accuracy of the attained AASs by making some graphical and numerical comparisons with their corresponding exact solutions and other existing equivalent AASs. The result of this article confirm that the efficiency, appropriateness and time spent capability of the newly constructed AFVI method are better than that of the other existing analogous fractional analytical approximation methods. Here, we apply the Maple 2021 programming software to obtain the AASs of the formulated IVPs and drawing the 3D graphs of the attained AASs. Finally, in this article we validate the applicability of the Caputo fractional order derivative to form a novel analytical approximation method as well as to fractionalize some essential NLEEs of Mathematical physics.

在本文中，我们构建并研究了一种新的分数变分迭代技术，并将其命名为 AFVI 方法。随后，我们提出了一些与分数非线性演化方程 NLTFFWE、mNLTFFWE、TFmCHE 和 TFmDPE 相对应的 IVPs。卡普托分数阶导数被用来对所考虑的非线性演化方程进行分数化。然后，我们应用所制定的 AFVI 方法求解所考虑的 IVP。最后，我们通过与相应的精确解和其他现有等效 AAS 进行图形和数值比较，检验了所获得 AAS 的准确性。本文的结果证实，新构建的 AFVI 方法的效率、适当性和耗时能力均优于其他现有的类似分数解析近似方法。在此，我们应用 Maple 2021 编程软件获取了所制定的 IVP 的解析近似值，并绘制了解析近似值的三维图形。最后，我们在本文中验证了 Caputo 分数阶导数的适用性，以形成一种新颖的分析近似方法，并对数学物理中的一些基本 NLEE 进行分数化。

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引用次数: 0

Computational analysis of radiative flow of power law fluid with heat generation effects: Galerkin finite element simulations 具有发热效应的幂律流体辐射流计算分析：伽勒金有限元模拟

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-22 DOI: 10.1016/j.padiff.2024.100927

This research aims to presents the free convective flow power law fluid due to vertical cone. The investigation for observing the heat transfer phenomenon is accounted to heat generation and radiative effects. The assumption of variable viscosity is taken into account. A vertical cone induced the flow. The dimensionless variables are followed to attains the simplified form. The numerical computations are performed with help of famous finite element method (FEM). The FEM algorithm is supported with applications of quadratic Lagrange polynomials. The results are confirmed with peak accuracy. The physical aspect of problem is presented in view of shear thickening, shear thinning and viscous material case. A comparative thermal reflection in absence and presence of heat generation have been endorsed. Moreover, the insight of various parameters on Nusselt number is also presented.

本研究旨在介绍垂直锥体导致的自由对流幂律流体。观察传热现象的研究考虑了热量产生和辐射效应。同时考虑了粘度可变的假设。垂直锥体诱导流动。采用无量纲变量，以达到简化形式。数值计算采用著名的有限元法（FEM）。有限元算法应用了二次拉格朗日多项式。计算结果的精确度达到了顶峰。从剪切增厚、剪切减薄和粘性材料的角度介绍了问题的物理方面。在不产生热量和产生热量的情况下，对热反射进行了比较。此外，还介绍了各种参数对努塞尔特数的影响。

引用次数: 0

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