Partial Differential Equations in Applied Mathematics最新文献_第5页

Higher dimensional nonlinear model arising to the diversity of fields: Dynamics of wave structures with M-fractional derivative 由场的多样性引起的高维非线性模型：具有m阶导数的波结构动力学

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-09-15 DOI: 10.1016/j.padiff.2025.101284

Usman Younas , Jan Muhammad , Ejaz Hussain

{"title":"Higher dimensional nonlinear model arising to the diversity of fields: Dynamics of wave structures with M-fractional derivative","authors":"Usman Younas , Jan Muhammad , Ejaz Hussain","doi":"10.1016/j.padiff.2025.101284","DOIUrl":"10.1016/j.padiff.2025.101284","url":null,"abstract":"<div><div>In this work, we investigates the dynamics of waves of a higher dimensional nonlinear partial differential equation known as P-type (3+1)-dimensional model. This model is employed for modeling plasma waves and instabilities in plasma physics. In the context of quantum field theory and other domains, the (3+1)-dimensional p-type model is a theoretical construct that is employed to investigate a diverse array of physical processes. In addition to magnetism and the conventional theory of particle physics, this model elucidates the specific proper ties of materials and spontaneous processes in solid-state structures. In this study, we utilize the M-fractional derivative and an appropriate wave transformation for converting the governing equation into an ordinary differential equation, thereby attaining the desired exact solutions. The generalized Arnous method, F-expansion approach, and Kumar–Malik method are employed to acquire solutions. By employing these techniques, a variety of solutions are attained, such as combined, bright, dark, bright and dark, mixed, and singular solitons. The model under investigation contains a significant number of soliton solution structures. Moreover, we represent the behaviors of the solutions in 2D and 3D graphs using the appropriate parameter values. The findings presented in this study can improve the nonlinear dynamical characteristics of a specific system and validate the efficacy of the used methodologies. Our findings provide useful insights into the intricacy of nonlinear equations, enhancing prior research on the subject through the introduction of innovative techniques and the discovery of a significant number of solutions that have wide-ranging relevance.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101284"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108166","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

Numerical exploration for bioconvective nanofluid flow towards a rotating surface with chemical reaction and radiative effects 具有化学反应和辐射效应的旋转表面生物对流纳米流体流动的数值探索

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-10-14 DOI: 10.1016/j.padiff.2025.101310

Tooba Sadaf , Ali B.M. Ali , Sami Ullah Khan , M. Ijaz Khan , Nidhal Ben Khedher

引用次数: 0

Generalised Kolmogorov-Petrovskii-Piskunov equation of fractional order: Power series and shifted Legendre collocation methods 分数阶广义Kolmogorov-Petrovskii-Piskunov方程：幂级数和移位Legendre配置方法

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-10-20 DOI: 10.1016/j.padiff.2025.101318

Richard Olu Awonusika, Abayomi Samuel Oke

{"title":"Generalised Kolmogorov-Petrovskii-Piskunov equation of fractional order: Power series and shifted Legendre collocation methods","authors":"Richard Olu Awonusika, Abayomi Samuel Oke","doi":"10.1016/j.padiff.2025.101318","DOIUrl":"10.1016/j.padiff.2025.101318","url":null,"abstract":"<div><div>The classical Kolmogorov-Petrovskii-Piskunov (KPP) equation describes physical phenomena such as combustion, chemical reaction, evolution of dominant genes, and propagation of nerve pulses. In this paper, we present solutions of a time-fractional order generalised KPP equation using a power series method and Legendre collocation method. The fractional order derivative is described in the Caputo sense. The proposed power series method assumes that the solution of the governing problem can be represented by a fractional power series in time variable, with space-variable expansion coefficients. The nonlinear term is assumed to be analytic in the unknown, and thus, admits a power series representation. The generalised Cauchy product is applied to transform the power series in the unknown to one in the time-dependent variable. An explicit recursion formula for the variable expansion coefficient is then constructed. On the other hand, the shifted Legendre collocation method assumes that the solution of the proposed problem can be expressed as a shifted Legendre polynomial series, with constant expansion coefficients to be determined. Collocating at the shifted Legendre-Gauss nodes, we obtain a set of nonlinear algebraic equations. These algebraic equations are then solved for the unknown Legendre expansion coefficients using Newton’s iteration method. Convergence analyses of both methods are presented. Examples of the proposed problem involving quadratic, cubic, and exponential nonlinearities are considered to demonstrate the efficiency, accuracy, and reliability of the proposed techniques. The results obtained from both methods are in excellent agreement with the exact solutions.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101318"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466070","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

Spatially localized trains of soliton in attractive Bose-Einstein condensates with periodic potential 具有周期势的吸引玻色-爱因斯坦凝聚体中的空间定域孤子列

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-11-14 DOI: 10.1016/j.padiff.2025.101322

Nkeh Oma Nfor , Akoni Brikly Njinabo , Francois Marie Moukam Kakmeni

{"title":"Spatially localized trains of soliton in attractive Bose-Einstein condensates with periodic potential","authors":"Nkeh Oma Nfor , Akoni Brikly Njinabo , Francois Marie Moukam Kakmeni","doi":"10.1016/j.padiff.2025.101322","DOIUrl":"10.1016/j.padiff.2025.101322","url":null,"abstract":"<div><div>We investigate the spatial profiles of periodic localized modes in attractive Bose-Einstein condensates, by solving the mean-field Gross-Pitaevskii equation in the presence of elliptic-type periodic potential. By considering a one-dimensional time independent linearized Gross-Pitaevskii equation, we obtained three bound state solutions and energies emanating from the first order Lamé equation. When the nonlinearity induced by the two body inter-atomic interactions are fully activated, spatially localized trivial phase periodic solutions of the attractive condensates are analytically obtained using the ansatz technique coupled with the direct integral method. Results of numerical simulation depicts trivial phase solutions, which are uniform train of spatially localized modes that are insensitive to variation of the elliptic modulus. However in the non-trivial phase regime, the spatially localized trains of soliton become very structurally unstable. This work underscores the spontaneous generation of periodic potential by the condensate wave function, determine the band structure of the lattice and basic properties of periodic matter waves under linear conditions, and highlight various spatial nonlinear periodic modes in the condensate. Finally, our investigation provides a solid theoretical framework that finds potential application in the fabrication of atomic lasers, periodic matter-wave gratings and quantum logic gates.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101322"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145576324","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

New global regularity result for the 3D incompressible Navier–Stokes equations 三维不可压缩Navier-Stokes方程的新的全局正则性结果

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-09-26 DOI: 10.1016/j.padiff.2025.101306

Abdelhafid Younsi

引用次数: 0

Building novel solitary wave solutions for the generalized non-linear (3+1)-dimensional wave equation with gas bubbles in fluids using an analytic method 用解析法建立流体中含气泡的广义非线性（3+1）维波动方程的孤波解

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-09-08 DOI: 10.1016/j.padiff.2025.101272

Abeer S. Khalifa , Niveen M. Badra , Hamdy M. Ahmed , Wafaa B. Rabie , Homan Emadifar , Karim K. Ahmed

{"title":"Building novel solitary wave solutions for the generalized non-linear (3+1)-dimensional wave equation with gas bubbles in fluids using an analytic method","authors":"Abeer S. Khalifa , Niveen M. Badra , Hamdy M. Ahmed , Wafaa B. Rabie , Homan Emadifar , Karim K. Ahmed","doi":"10.1016/j.padiff.2025.101272","DOIUrl":"10.1016/j.padiff.2025.101272","url":null,"abstract":"<div><div>This article investigates the generalized nonlinear (3+1)-dimensional wave equation using an analytical technique — the Extended F-expansion method — to derive a variety of exact wave solutions and analyze the dynamic behavior of distinct wave profiles. The study presents several types of soliton solutions, including dark, bright, singular, periodic, and singular periodic forms. To the best of our knowledge, these specific solutions have not been previously reported in the literature. By assigning appropriate values to the free parameters, the behavior of the obtained solutions is illustrated through two- and three-dimensional plots, as well as corresponding contour diagrams. The proposed analytical method not only contributes to the theoretical understanding of nonlinear wave phenomena but also demonstrates practical relevance in applied sciences, particularly in fluid mechanics and engineering contexts involving gas-liquid interactions.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101272"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061380","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

Improved explicit finite difference method for extended shallow water partial differential equation 扩展浅水偏微分方程的改进显式有限差分法

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-10-17 DOI: 10.1016/j.padiff.2025.101316

Saeed Ahmed Rajput , Shakeel Ahmed Kamboh , Khuda Bux Amur , Afaque Ahmed Bhutto

{"title":"Improved explicit finite difference method for extended shallow water partial differential equation","authors":"Saeed Ahmed Rajput , Shakeel Ahmed Kamboh , Khuda Bux Amur , Afaque Ahmed Bhutto","doi":"10.1016/j.padiff.2025.101316","DOIUrl":"10.1016/j.padiff.2025.101316","url":null,"abstract":"<div><div>The shallow water and Boussinesq equations, being highly nonlinear coupled partial differential equations, form a significant basis for the simulation of flow phenomena within the surface and subsurface domains. The application of these equations extends into several fields in the area of engineering and science, including the simulation of Kelvin wake waves, scenarios involving dam break, propagation of flood waves and flow over a bump. In this paper, the shallow water equation for surface flow regions and the Boussinesq partial differential equation for subsurface flow regions are unified into a single set of extended shallow water nonlinear partial differential equations which is applicable for both flow domains. These equations are solved numerically using an improved two-step Lax-Wendroff method with sixth-order accuracy. The method is validated by benchmarking against existing experimental data, which shows a percentage error of less than 1%, confirming its high accuracy and reliability. Moreover, the method is applied to two test cases. The first case is flow over a bump, where the relative error for surface and subsurface flow regions is as low as 10<sup>−8</sup> at <em>t</em> = 100. In the second case, Kelvin wake wave is investigated with the improved sixth-order Lax-Wendroff scheme predicting an arm angle of 20.6955°, while a theoretical particle angle of 19.47° was observed. The results show that this method is good enough and useful for the simulation of surface and subsurface flows phenomena.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101316"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362456","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

Entropy generation and MHD flow characteristics of unsteady Williamson fluid toward a stagnation point over a vertical Riga plate 竖直Riga板上非定常Williamson流体滞止点的熵生和MHD流动特性

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-11-20 DOI: 10.1016/j.padiff.2025.101321

Hassan Shahzad , Dur-E-Shehwar Sagheer , Hajra Batool , Maryam Ali Alghafli , Nabil Mlaiki

{"title":"Entropy generation and MHD flow characteristics of unsteady Williamson fluid toward a stagnation point over a vertical Riga plate","authors":"Hassan Shahzad , Dur-E-Shehwar Sagheer , Hajra Batool , Maryam Ali Alghafli , Nabil Mlaiki","doi":"10.1016/j.padiff.2025.101321","DOIUrl":"10.1016/j.padiff.2025.101321","url":null,"abstract":"<div><div>This study presents a mathematical model to explore two-dimensional, time-dependent fluid flow towards a stagnation point over a Riga plate, under the influence of magnetohydrodynamics (MHD), activation energy, and a higher-order chemical reaction. The surface of the Riga plate is lined with magnets and electrodes, arranged in a structured manner. The research investigates the effects of radiation and Joule heating on fluid motion and includes an entropy generation analysis based on the second law of thermodynamics. The partial differential equations (PDEs) that govern the physical system are reduced to ordinary differential equations (ODEs) via similarity variables, and solved using both the shooting method and the bvp4c algorithm. Results indicate that the unsteadiness parameter increases skin friction by 5.53 %, while the heat source parameter reduces heat transfer by up to 33.4 %. Entropy generation is found to rise with increasing Brinkman number and concentration difference, whereas higher temperature differences lower entropy production. The combined effects of Lorentz force, exponential chemical reaction, internal heat generation, and suction/injection within an unsteady Riga plate configuration have not been explored previously. Furthermore, the inclusion of irreversibility analysis enhances the novelty and provides deeper insight into energy dissipation mechanisms and system efficiency, offering valuable guidance for designing advanced MHD-based thermal control and energy systems. These numerical results are well aligned with existing literature, reinforcing the reliability of the analysis and highlighting its significance for energy-efficient thermal system design.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101321"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145623825","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

Dynamics and modeling of Malaria disease with vector mortality rate and host transmission by using Piecewise Fractional Operator 基于分段分数算子的疟疾病媒死亡率和宿主传播动力学与建模

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-10-16 DOI: 10.1016/j.padiff.2025.101309

Muhammad Farman , Saba Jamil , Evren Hincal , Ali Akgul , Muhammad Umer Saleem , Dumitru Baleanu

{"title":"Dynamics and modeling of Malaria disease with vector mortality rate and host transmission by using Piecewise Fractional Operator","authors":"Muhammad Farman , Saba Jamil , Evren Hincal , Ali Akgul , Muhammad Umer Saleem , Dumitru Baleanu","doi":"10.1016/j.padiff.2025.101309","DOIUrl":"10.1016/j.padiff.2025.101309","url":null,"abstract":"<div><div>Malaria remains one of the most persistent vector-borne diseases, requiring advanced modeling tools to capture its complex transmission dynamics. This study introduces a novel piecewise Caputo fractional operator with a singular kernel to model malaria transmission between humans and mosquito vectors. The proposed operator allows the system to switch between different fractional dynamics across subintervals, thereby capturing sudden behavioral or environmental changes an ability not present in traditional fractional- or integer-order models. The existence and uniqueness of the systems solutions are rigorously established using the Arzelà–Ascoli and Schauder fixed-point theorems, ensuring mathematical validity. The basic reproduction number is derived via the next-generation matrix approach and analyzed through sensitivity indices to identify key epidemiological parameters influencing transmission. Furthermore, the generalized Ulam–Hyers stability confirms robustness under small perturbations. Numerical simulations based on the Newton polynomial scheme reveal crossover behavior between subintervals and demonstrate that lower fractional orders intensify memory effects, leading to delayed but more stable epidemic responses. Overall, the piecewise Caputo framework enhances the modeling of malaria dynamics by integrating memory-dependent and regime-switching properties, offering a more biologically realistic approach to designing and timing intervention strategies.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101309"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325714","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

Analyzing dynamics of a heterogeneous reaction convection diffusion COVID-19 model with vaccination effects 考虑疫苗接种效应的非均质反应对流扩散COVID-19模型动力学分析

Partial Differential Equations in Applied Mathematics Pub Date : 2025-12-01 Epub Date: 2025-10-01 DOI: 10.1016/j.padiff.2025.101308

Tasmia Hoque , Samir Kumar Bhowmik

{"title":"Analyzing dynamics of a heterogeneous reaction convection diffusion COVID-19 model with vaccination effects","authors":"Tasmia Hoque , Samir Kumar Bhowmik","doi":"10.1016/j.padiff.2025.101308","DOIUrl":"10.1016/j.padiff.2025.101308","url":null,"abstract":"<div><div>Mathematical models are fundamental tools for understanding the dynamics of infectious disease transmission and for guiding effective control strategies. In this study, we extend existing COVID-19 models by incorporating a risk-dependent (variable) vaccination policy, heterogeneity in individual susceptibility, and spatial diffusion effects. The model is formulated through a system that combines ordinary and partial differential operators, allowing us to capture both population-level dynamics and spatial variability. Specifically, we introduce vaccination rates that vary with individual risk, reflecting real-world prioritization strategies where highly vulnerable groups are targeted first. This extension provides a more realistic representation of epidemic control measures and allows the study of how different vaccination efforts alter disease trajectories. Numerical simulations demonstrate that risk-based vaccination strategies significantly influence epidemic patterns, including the emergence of rebounds, shoulders, and oscillations in infection prevalence. Our findings highlight the critical role of variable vaccination, heterogeneous risk structures, and spatial diffusion in shaping epidemic outcomes. They also provide insights into how adaptive and risk-sensitive vaccination strategies can mitigate transmission more effectively under realistic conditions of variability.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101308"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268620","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