Partial Differential Equations in Applied Mathematics最新文献_第7页

Mathematical model of immune response to Hepatitis C virus (HCV) disease 丙型肝炎病毒（HCV）疾病免疫反应的数学模型

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-09-13 DOI: 10.1016/j.padiff.2025.101275

Amna H.A. Ibrahim, Hermane Mambili Mamboundou

{"title":"Mathematical model of immune response to Hepatitis C virus (HCV) disease","authors":"Amna H.A. Ibrahim, Hermane Mambili Mamboundou","doi":"10.1016/j.padiff.2025.101275","DOIUrl":"10.1016/j.padiff.2025.101275","url":null,"abstract":"<div><div>This paper presents a mathematical model that comprehensively analyzes the dynamics of Hepatitis C Virus (HCV) infection. The model based on a system of nonlinear differential equations captures the interactions between liver cells (hepatocytes), the Hepatitis C virus, immune cells, and cytokines dynamics. We establish the well-posedness of the model within a biologically feasible region. Using the next-generation method, we calculate the basic reproduction number, <span><math><msub><mrow><mi>ℜ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, a threshold parameter that determines whether the infection will spread or die. A sensitivity analysis is also performed to identify the parameters that most significantly influence this number. We derive the conditions for the stability of disease-free and endemic equilibrium. The model is then used to investigate the system’s behavior under various scenarios: a weak immune response, the absence of T helper cell support, and a strong immune response. Our simulations show that the lack of interleukin-2 (IL-2) significantly affects the activation of cytotoxic T lymphocyte (CTLs). These results underscore the importance of including T helper cells, Interferon<span><math><mrow><mo>−</mo><mi>γ</mi></mrow></math></span> (IFN-<span><math><mi>γ</mi></math></span>) and IL-2 for an accurate representation of the dynamics of hepatitis C virus infection. Ultimately, this study deepens our understanding of the dynamics of HCV infection and simplifies how specific immune components shape the course of the disease.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101275"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Intrinsic dynamics of lumps and multi-soliton solutions to the higher dimensional Boussinesq model 块的内在动力学和高维Boussinesq模型的多孤子解

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-10-21 DOI: 10.1016/j.padiff.2025.101320

M. Belal Hossen , Md. Towhiduzzaman , Mst. Shekha Khatun , Harun-Or- Roshid , Md. Amanat Ullah

引用次数: 0

Dynamic complexity in fractional multispecies ecological systems: A Caputo derivative approach 分数多物种生态系统的动态复杂性：卡普托导数方法

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-09-10 DOI: 10.1016/j.padiff.2025.101293

Sonal Jain , Kolade M. Owolabi , Edson Pindza , Eben Mare

{"title":"Dynamic complexity in fractional multispecies ecological systems: A Caputo derivative approach","authors":"Sonal Jain , Kolade M. Owolabi , Edson Pindza , Eben Mare","doi":"10.1016/j.padiff.2025.101293","DOIUrl":"10.1016/j.padiff.2025.101293","url":null,"abstract":"<div><div>In this study, a novel implicit numerical approach is introduced by combining finite-difference techniques with innovative L1 schemes. This method is designed to solve time-fractional reaction–diffusion systems occurring in one and two dimensions. Specifically, the focus is on ecological systems with mixed boundary conditions, which are commonly found in biological and chemical processes. This research focuses on the spatiotemporal behavior of a predator–prey model with a Holling III functional response, taking into account the presence of prey refuges. This study revealed that this model does not exhibit a Turing pattern, which is typically associated with diffusion-driven instability. Consequently, this investigation explored alternative non-Turing patterns using extensive numerical simulations. In scenarios involving two-dimensional subdiffusion, the study observed a variety of spatiotemporal dynamics within the diffusive prey–predator model. When prey refuge availability was low, the system displayed a circular pattern that gradually expanded over time to encompass the entire spatial domain. As the availability of refugees decreased, the system transitioned from a spiral to a chaotic pattern. Furthermore, the research revealed that, as the ratio of predator-to-prey diffusion rates increased, the system exhibited a subdiffusive spiral pattern, which then transformed into a spot-like pattern. Eventually, these spots merged to form stripe-like patterns as the ratio increased. This investigation highlights the rich and intricate dynamics that can emerge in fractional predator–prey interactions when considering both spatial and temporal factors. To further confirm the complexity of the dynamical behaviors, Lyapunov exponents were estimated numerically.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101293"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Invariant formulation of nonclassical symmetries and explicit solutions of Rosenau-Hyman equation along with bifurcation analysis Rosenau-Hyman方程非经典对称的不变量表述和显式解及其分岔分析

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-10-19 DOI: 10.1016/j.padiff.2025.101314

M.A. El-Shorbagy , Sonia Akram , Mati Ur Rahman , Hossam A. Nabwey

{"title":"Invariant formulation of nonclassical symmetries and explicit solutions of Rosenau-Hyman equation along with bifurcation analysis","authors":"M.A. El-Shorbagy , Sonia Akram , Mati Ur Rahman , Hossam A. Nabwey","doi":"10.1016/j.padiff.2025.101314","DOIUrl":"10.1016/j.padiff.2025.101314","url":null,"abstract":"<div><div>This study focuses on the Rosenau–Hyman equation, which is a fundamental model in nonlinear wave dynamics, and investigates it through the lens of nonclassical symmetry analysis. The approach employs symbolic computation to derive determining equations and uncover new invariant formulations, from which several explicit exact solutions are constructed. To further understand the system’s behavior, dynamical tools such as bifurcation analysis, sensitivity tests, Lyapunov exponents, and phase portraits are applied, highlighting the presence of stability transitions, multistability, and chaotic regimes. In addition, travelling wave solutions are obtained using the enhanced modified extended tanh function method (eMETFM), providing complementary wave structures. The findings deepen our understanding of nonlinear dispersive wave propagation and soliton interactions, with particular relevance to shallow water dynamics. More broadly, the developed solutions and their graphical interpretations contribute valuable insights for theoretical studies and applied research in fluid dynamics and wave modeling.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101314"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exploration of the Arrhenius activation energy in unsteady ternary hybrid nanofluid flow past a slendering stretching sheet: RSM analysis 非定常三元杂化纳米流体通过细长拉伸片的阿伦尼乌斯活化能探索：RSM分析

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-07-14 DOI: 10.1016/j.padiff.2025.101255

N. Nithya , B. Vennila , K. Loganathan , R. Shobika , K. Senthilvadivu , S. Eswaramoorthi

{"title":"Exploration of the Arrhenius activation energy in unsteady ternary hybrid nanofluid flow past a slendering stretching sheet: RSM analysis","authors":"N. Nithya , B. Vennila , K. Loganathan , R. Shobika , K. Senthilvadivu , S. Eswaramoorthi","doi":"10.1016/j.padiff.2025.101255","DOIUrl":"10.1016/j.padiff.2025.101255","url":null,"abstract":"<div><div>This paper examines how a ternary hybrid nanofluid made by combining <span><math><msub><mrow><mtext>TiO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>, <span><math><msub><mrow><mtext>SiO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>, and <span><math><mrow><msub><mrow><mtext>Al</mtext></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mtext>O</mtext></mrow><mrow><mn>3</mn></mrow></msub></mrow></math></span> in water behaves when flowing across a stretching sheet with varying thickness. The motivation comes from real world needs in systems like solar collectors, biomedical devices, and industrial cooling, where better heat transfer with minimal drag is essential. Using a blend of the Differential Transformation Method (DTM) and statistical optimization techniques like Response Surface Methodology (RSM) and Central Composite Design (CCD), we study how magnetic field, radiation, nanoparticle volume fraction, and activation energy affects the system. The hybrid nanofluid’s improved thermal behavior is a key focus. It is found that the increasing sheet thickness leads to higher temperatures, while velocity and concentration drop. Greater thermal radiation and more silicon dioxide particles enhance the heat transfer, improving efficiency by 12% and reducing drag (skin friction) by 15% under optimized conditions. Thermal conductivity improves with more nanoparticles, raising the Nusselt number. Meanwhile, mass diffusion behavior captured by the Sherwood number is influenced by activation energy and the Schmidt number. Magnetic field and nanoparticle volume fraction effects together help lower surface drag.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101255"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Machine learning analysis of tangent hyperbolic nanofluid with radiation and Arrhenius activation energy over falling cone under gravity 重力作用下落锥上具有辐射和Arrhenius活化能的正切双曲纳米流体的机器学习分析

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-08-22 DOI: 10.1016/j.padiff.2025.101280

Muhammad Zubair , Hamid Qureshi , Usman Khaliq , Taoufik Saidani , Waqar Azeem Khan

{"title":"Machine learning analysis of tangent hyperbolic nanofluid with radiation and Arrhenius activation energy over falling cone under gravity","authors":"Muhammad Zubair , Hamid Qureshi , Usman Khaliq , Taoufik Saidani , Waqar Azeem Khan","doi":"10.1016/j.padiff.2025.101280","DOIUrl":"10.1016/j.padiff.2025.101280","url":null,"abstract":"<div><div>This study is a machine learning investigation of the advance level nanofluidic coolant through a cone in a two-dimensional transitory boundary layer. The model accounts for both radiation absorption and the Arrhenius activation energy. Synthetic datasets from governing mathematical model are used in Artificial Intelligence (AI) based Levenberg Marquardt Back Propagation algorithm (LM-BP). Multiple scenarios of Tangent Hyperbolic Nanofluidic (THNF) coolant are framed with variation of influencing characteristics like Magnetic field <em>M</em>, power law index <em>n</em>, permeability <em>k</em>, Radiation absorption <em>Q</em>, Prandtl ratio <em>Pr</em>, Brownian motion <em>Nb</em>, Lewis number <em>Le</em> and Chemical reaction parameter γ. Convergence parameters of AI-based feed routing Neural Network computing is presented through graphs and numerical tables. Results indicate that flow slows when the Lorentz force and surface permeability grow, but it gets stronger when thermal absorption and momentum to thermal diffusivity ratio Pr increase. Meanwhile, the temperature increases when thermal absorption rises and drops when thermal to mass diffusivity ratio Le increases so that temperature falls for greater chemical reaction influence.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101280"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144920092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Non-uniqueness of the solution of the Cauchy problem for one higher-order equation with a fractional derivative 具有分数阶导数的高阶方程Cauchy问题解的非唯一性

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-07-04 DOI: 10.1016/j.padiff.2025.101252

B. Yu. Irgashev , H.H. Pulatova

引用次数: 0

A study on intuitionistic fuzzy neutral functional integro-differential PDEs with impulses 带有脉冲的直觉模糊中立泛函积分微分偏微分方程的研究

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-08-25 DOI: 10.1016/j.padiff.2025.101296

T. Gunasekar , K. Nithyanandhan , Hanumagowda B. N , Jagadish V. Tawade , Nashwan Adnan Othman , Barno Abdullaeva , Nadia Batool , Khayrilla Kurbonov

{"title":"A study on intuitionistic fuzzy neutral functional integro-differential PDEs with impulses","authors":"T. Gunasekar , K. Nithyanandhan , Hanumagowda B. N , Jagadish V. Tawade , Nashwan Adnan Othman , Barno Abdullaeva , Nadia Batool , Khayrilla Kurbonov","doi":"10.1016/j.padiff.2025.101296","DOIUrl":"10.1016/j.padiff.2025.101296","url":null,"abstract":"<div><div>This paper investigates the existence and uniqueness of solutions for a nonlocal intuitionistic fuzzy impulsive integro-differential equation, employing intuitionistic fuzzy semigroups and the contraction mapping principle. Through a systematic theoretical framework, it establishes that, under certain conditions, a distinct solution is ensured. Additionally, the study expands its analysis to explore the existence results for intuitionistic fuzzy impulsive neutral integro-differential equations, broadening its research focus. This approach introduces a new perspective on understanding intuitionistic fuzzy integro-differential equations, introducing innovative methodologies and significant discoveries that advance theoretical exploration in this field. The findings underscore that, subject to specific assumptions, a singular fuzzy solution emerges for these problems marked by nonlocal conditions, effectively addressing crucial challenges in the analysis of fuzzy systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101296"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An enhanced Artificial Neural Network approach for solving nonlinear fractional-order differential equations 求解非线性分数阶微分方程的增强人工神经网络方法

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-06-18 DOI: 10.1016/j.padiff.2025.101230

Nikhil Sharma , Sunil Joshi , Pranay Goswami

引用次数: 0

Stochastic reynolds equation for magnetohydrodynamics micropolar fluid and surface roughness in squeeze-film lubrication characteristics of rough parallel rectangular plates 粗糙平行矩形板挤压膜润滑特性中微极流体和表面粗糙度的随机reynolds方程

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-08-05 DOI: 10.1016/j.padiff.2025.101269

B.S. Asha , H.M. Shivakumar , B.N. Hanumagowda , Jagadish V. Tawade , Barno Abdullaeva , Manish Gupta , Murali Gundagani , Taoufik Saidani , Nadia Batool

{"title":"Stochastic reynolds equation for magnetohydrodynamics micropolar fluid and surface roughness in squeeze-film lubrication characteristics of rough parallel rectangular plates","authors":"B.S. Asha , H.M. Shivakumar , B.N. Hanumagowda , Jagadish V. Tawade , Barno Abdullaeva , Manish Gupta , Murali Gundagani , Taoufik Saidani , Nadia Batool","doi":"10.1016/j.padiff.2025.101269","DOIUrl":"10.1016/j.padiff.2025.101269","url":null,"abstract":"<div><div>This study presents a comprehensive theoretical investigation into the influence of surface roughness, magnetohydrodynamics (MHD), and micropolar fluid dynamics on the squeeze film behavior between two wide, parallel rectangular plates. A modified Reynolds equation is derived by incorporating Eringen’s microcontinuum theory, Christensen’s stochastic surface roughness model, and classical hydrodynamic principles. The model accounts for the effects of a perpendicular magnetic field and longitudinal surface irregularities. Key performance parameters—namely pressure distribution, load-carrying capacity, and squeeze film duration—are obtained analytically and evaluated using dimensionless groups such as the Hartmann number, coupling number, fluid gap interaction number, and surface roughness parameter. The results demonstrate that incorporating micropolar fluid properties and MHD effects significantly enhances squeeze film performance compared to the Newtonian fluid case. Surface roughness is also found to play a beneficial role in improving load support and film retention. The findings offer valuable insights for designing advanced lubrication systems in engineering applications where microstructural effects and magnetic fields are present.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101269"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0