Partial Differential Equations in Applied Mathematics最新文献_第2页

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

Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-27 DOI: 10.1016/j.padiff.2024.100939

{"title":"Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method","authors":"","doi":"10.1016/j.padiff.2024.100939","DOIUrl":"10.1016/j.padiff.2024.100939","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419616","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

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

Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-27 DOI: 10.1016/j.padiff.2024.100938

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

Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-26 DOI: 10.1016/j.padiff.2024.100934

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

Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-25 DOI: 10.1016/j.padiff.2024.100942

{"title":"Mathematical analysis of soliton solutions in space-time fractional Klein-Gordon model with generalized exponential rational function method","authors":"","doi":"10.1016/j.padiff.2024.100942","DOIUrl":"10.1016/j.padiff.2024.100942","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357948","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

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

Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-25 DOI: 10.1016/j.padiff.2024.100933

{"title":"Nonlinear dynamics model of HIV/AIDS: Assessing the impacts of condoms, vaginal microbicides, and optimized treatment","authors":"","doi":"10.1016/j.padiff.2024.100933","DOIUrl":"10.1016/j.padiff.2024.100933","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357949","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 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

Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-24 DOI: 10.1016/j.padiff.2024.100918

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

Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-24 DOI: 10.1016/j.padiff.2024.100941

{"title":"Entropy analysis in magnetized blood-based hybrid nanofluid flow via parallel disks","authors":"","doi":"10.1016/j.padiff.2024.100941","DOIUrl":"10.1016/j.padiff.2024.100941","url":null,"abstract":"<div><div>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 Fe<sub>3</sub>O<sub>4</sub> 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.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357870","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

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

Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-24 DOI: 10.1016/j.padiff.2024.100940

{"title":"Numerical illustration using finite difference method for the transient flow through porous microchannel and statistical interpretation of entropy using response surface methodology","authors":"","doi":"10.1016/j.padiff.2024.100940","DOIUrl":"10.1016/j.padiff.2024.100940","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419538","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 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

Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-23 DOI: 10.1016/j.padiff.2024.100937

{"title":"Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI method","authors":"","doi":"10.1016/j.padiff.2024.100937","DOIUrl":"10.1016/j.padiff.2024.100937","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328354","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 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

Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-22 DOI: 10.1016/j.padiff.2024.100927

引用次数: 0