Partial Differential Equations in Applied Mathematics最新文献

{"title":"Septic-order triangular finite elements: An explicit method with cubic arc subparametric transformations","authors":"G. Shylaja ,&nbsp;V. Kesavulu Naidu ,&nbsp;B. Venkatesh ,&nbsp;S.M. Mallikarjunaiah","doi":"10.1016/j.padiff.2025.101332","DOIUrl":"10.1016/j.padiff.2025.101332","url":null,"abstract":"<div><div>This paper presents an explicit integration scheme that incorporates septic-order triangular elements. Cubic arcs are utilized to approximate the curved edges of these elements. This methodology is particularly effective for discretizing curved domains, and its primary objective is the approximation of equations involving differential operators. A 36-node septic-order triangular element with a curved boundary, which consists of one curved edge and two straight edges, is introduced in this study. This element serves as the foundation for the isoparametric coordinate transformation discussed herein. A standard triangle in the local coordinate system is mapped onto the curved triangular element in the global coordinate system by means of a unique point transformation. The curved triangular element is replaced by septic arcs, and the coordinates located on the curved edge are embedded within the parameters that define these arc equations. Each arc consistently represents a distinct cubic arc due to the relationships involved in the parameter calculations. Consequently, the overall numerical approximation is highly accurate. For higher-order curved triangular elements, the finite element method, in conjunction with numerical integration that utilizes curved boundary point transformations (applicable to both the exterior and interior of each curved triangular element), will act as a robust subparametric coordinate transformation and, as a result, a formidable numerical technique. The efficacy of this method is demonstrated through the resolution of three boundary value problems. Numerical outcomes affirm that the proposed technique significantly surpasses existing methods in the approximation of boundary value problems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101332"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791937","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}

{"title":"On certain surface integrals related to the conormal derivative problem","authors":"Dian K. Palagachev","doi":"10.1016/j.padiff.2025.101325","DOIUrl":"10.1016/j.padiff.2025.101325","url":null,"abstract":"<div><div>The non-homogeneous conormal derivative problems for nonlinear, second-order divergence form elliptic equations with singular data appear naturally in mathematical modeling of real phenomena involving problems of image recovery, the thermistor problem, or studies of non-Newtonian fluids.</div><div>We prove suitable estimates for certain surface integrals, related to non-homogeneous conormal derivative problems, which lead to essential boundedness of the weak solutions under quite general hypotheses on the data.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101325"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145760656","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}

{"title":"Analysis of Navier slip effects in ionized power-law hybrid nanofluid flow through a Darcy–Forchheimer porous medium with modified Fourier heat transfer","authors":"Mehari Fentahun Endalew,&nbsp;Xiaoming Zhang","doi":"10.1016/j.padiff.2025.101299","DOIUrl":"10.1016/j.padiff.2025.101299","url":null,"abstract":"<div><div>Hybrid nanofluids have emerged as a promising medium for enhancing heat transfer, with power-law hybrid nanofluids (PLHNF) exhibiting superior thermal conductivity compared to conventional power-law nanofluids (PLNF). Despite these advantages, their transport behavior under complex flow conditions — particularly in ionized Darcy–Forchheimer regimes influenced by slip effects and non-classical heat conduction — remains largely unexplored. This study addresses this gap by developing a comprehensive theoretical framework for PLHNF flow over a stretching surface, incorporating magnetic field inclination, Navier slip, and a modified Fourier’s law of heat conduction. The governing nonlinear system is transformed via similarity techniques and solved numerically using MATLAB’s bvp4c solver, with validation against established benchmarks. The findings reveal that PLHNF not only sustain higher thermal transport but also exhibit distinctive flow responses: velocity slip significantly suppresses both axial and radial components, while inclined magnetic fields enhance axial transport but reduce radial motion. The superior thermal conductivity of PLHNF amplifies these effects, yielding higher surface heat transfer rates compared to PLNF. By elucidating the coupled influence of magnetic, slip, and non-Fourier heat conduction effects, this work extends the theoretical foundation of non-Newtonian hybrid nanofluids and highlights their potential for high-efficiency thermal management systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101299"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145119553","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}

{"title":"Heat transfer analysis of Ethylene Glycol based hybrid nanofluid (Au–Ag) flow over a porous medium with gyrotactic microorganisms: Levenberg–Marquardt backpropagation approach","authors":"R. Shobika ,&nbsp;B. Vennila ,&nbsp;K. Loganathan","doi":"10.1016/j.padiff.2025.101292","DOIUrl":"10.1016/j.padiff.2025.101292","url":null,"abstract":"<div><div>The proposed study employs the Levenberg–Marquardt backpropagation approach with artificial neural networks to examine the heat transfer in hybrid nanofluid flow over a porous embedded vertical stretching sheet in a Darcy–Forchheimer medium. This study seeks to investigate the interplay between gyrotactic microorganisms, magnetic fields, mixed convection, and temperature in hybrid nanofluids including Silver (Ag), Gold (Au), and the base fluid Ethylene Glycol <span><math><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mtext>H</mtext></mrow><mrow><mn>6</mn></mrow></msub><msub><mrow><mtext>O</mtext></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> utilizing the Cattaneo–Christov heat flux model. It improves our comprehension of their behavior and potential uses. This intricate system of highly non-linear governing equations is simplified to a set of ordinary differential equations by similarity transformations and solved numerically using the Bvp4c method. Alongside the numerical method, Artificial Neural Networks (ANNs) are utilized to precisely illustrate intricate patterns, with an Mean Square Error (MSE) of 0.00043 and strengthening the impact of the numerical findings. This study demonstrates that the utilization of Au–Ag/<span><math><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mtext>H</mtext></mrow><mrow><mn>6</mn></mrow></msub><msub><mrow><mtext>O</mtext></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> hybrid nanoparticles enhances thermal conductivity, augments volume fraction, and indicates that the application of a magnetic field and thermal radiation markedly improves the dispersion of microorganisms and the formation of hybrid nanofluids, resulting in elevated heat transfer rates. Especially, ANN-based regressor for sensitivity analysis is employed to forecast essential physical parameters, including the skin friction coefficient, Nusselt number, Sherwood number, and Density of Microorganisms, while also assessing the significance of factors affecting nanofluid properties, thereby demonstrating excellent concordance with prior studies and validating the robustness of the proposed model.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101292"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108165","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}

{"title":"Soliton propagation in optical metamaterials with nonlocal responses: A fractional calculus approach using (q,τ)-Mittag-Leffler functions","authors":"Shaher Momani ,&nbsp;Rabha W. Ibrahim","doi":"10.1016/j.padiff.2025.101305","DOIUrl":"10.1016/j.padiff.2025.101305","url":null,"abstract":"<div><div>This work investigates soliton solutions of nonlinear wave equations modeling light propagation in optical metamaterials with nonlocal nonlinear responses, incorporating external optical potentials. The residual power series method (RPSM) is employed to construct enhanced analytical solutions, capturing both dispersive and memory effects effectively. In addition, this study investigates the propagation of solitons in optical metamaterials with nonlocal responses using <span><math><mrow><mo>(</mo><mi>q</mi><mo>,</mo><mi>τ</mi><mo>)</mo></mrow></math></span>-fractional calculus. This calculus is based on the generalization of the quantum gamma function (<span><math><mrow><mrow><mo>(</mo><mi>q</mi><mo>,</mo><mi>τ</mi><mo>)</mo></mrow><mo>−</mo><mi>Γ</mi><mrow><mo>(</mo><mo>.</mo><mo>)</mo></mrow></mrow></math></span>). By employing <span><math><mrow><mo>(</mo><mi>q</mi><mo>,</mo><mi>τ</mi><mo>)</mo></mrow></math></span>-fractional derivatives in the form of the <span><math><mrow><mo>(</mo><mi>q</mi><mo>,</mo><mi>τ</mi><mo>)</mo></mrow></math></span>-Mittag-Leffler function, we explore the dynamics of soliton fields in these materials. The model considers key parameters such as the fractional order <span><math><mi>α</mi></math></span>, the generalized parameters <span><math><mi>q</mi></math></span> and <span><math><mi>τ</mi></math></span>, and the initial weight parameter <span><math><mi>β</mi></math></span>. The flexibility of these parameters allows for a more accurate description of optical metamaterials, capturing both classical soliton behavior and more complex nonlocal and memory effects. We compare fractional models with classical models and demonstrate the advantages of using fractional calculus to model memory effects and nonlocal interactions. Numerical simulations, including the residual series method, reveal the enhanced accuracy and insights provided by the fractional approach in optical metamaterials. The study provides a detailed framework for understanding soliton propagation in advanced optical materials, paving the way for the design of next-generation optical devices.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101305"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221956","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}

{"title":"Construction of an infinite-dimensional family of exact solutions of the Klein–Gordon equation by the hypercomplex method","authors":"Vitalii Shpakivskyi","doi":"10.1016/j.padiff.2025.101312","DOIUrl":"10.1016/j.padiff.2025.101312","url":null,"abstract":"<div><div>The Klein–Gordon equation is one of the fundamental equations of mathematical physics. Therefore, it is important to have exact solutions to this equation. There are many methods for constructing exact solutions to the Klein–Gordon equation. Naturally, that different methods give different exact solutions. In this paper, by the hypercomplex method, we construct an infinite-dimensional new family of exact solutions of the polynomial–exponential type to the Klein–Gordon equation.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101312"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145417310","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}

{"title":"Mathematical modeling for heat transportation analysis in hybrid nanofluid through a wedge surface under the influence of magnetic field","authors":"Bilal Ahmad,&nbsp;Muhammad Ozair Ahmed","doi":"10.1016/j.padiff.2025.101290","DOIUrl":"10.1016/j.padiff.2025.101290","url":null,"abstract":"<div><div>This study presents a mathematical model to analyze heat transport in a hybrid nanofluid composed of aluminum oxide (Al<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span>O<span><math><msub><mrow></mrow><mrow><mn>3</mn></mrow></msub></math></span>) and beryllium copper nanoparticles dispersed in water, flowing over a wedge-shaped surface under the influence of a transverse magnetic field. The formulation incorporates essential physical effects, including radiative heat transfer, activation energy, and chemical reaction kinetics, along with a nonlinear heat source. Using similarity transformations, the governing partial differential equations are reduced to a system of nonlinear ordinary differential equations, which are solved numerically via the fourth-order Runge–Kutta method combined with a shooting technique in <span>MATLAB</span>. The results reveal how magnetic intensity, nanoparticle concentration, and other dimensionless parameters affect the velocity, temperature, and concentration distributions. Significantly, the hybrid nanofluid demonstrates a 23% enhancement in thermal capacity, underscoring its potential to improve heat transfer performance. The computed skin friction, Nusselt number, and Sherwood number further validate the model and highlight its applicability to magnetically controlled thermal systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101290"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221966","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}

{"title":"Caputo approach to transmission dynamics of paragonimiasis in humans, snails, and crustaceans","authors":"Stephen Edward","doi":"10.1016/j.padiff.2025.101313","DOIUrl":"10.1016/j.padiff.2025.101313","url":null,"abstract":"<div><div><em>Paragonimiasis</em>, a parasitic infection caused by trematodes of the genus <em>Paragonimus</em>, is characterized by chronic cough, chest pain, and hemoptysis. This study introduces a novel fractional-order modelling technique to capture the impact of memory effects and control strategies on the transmission dynamics of <em>Paragonimiasis</em>. We develop a system of Caputo fractional differential equations supplemented with constant control measures–specifically, human treatment to reduce infection prevalence and snail molluscicide to target intermediate hosts. We analyze the fundamental properties of the model, including positivity, boundedness, existence, and uniqueness of solutions. Local stability of equilibrium states is investigated via Routh’s criterion, while Ulam-Hyer’s stability concepts confirm global stability. Numerical solutions obtained through the Adams-Bashforth-Moulton predictor-corrector method highlight the considerable influence of memory on disease progression. The results underscore the importance of integrating memory effects into control strategies: enhanced human treatment combined with improved snail molluscicide can significantly mitigate infection levels. These findings suggest that fractional derivatives offer a flexible, detailed lens for examining nonlocal disease dynamics processes and refining practical intervention approaches.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101313"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145525790","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}

{"title":"Buoyancy-induced nanofluid circulation in a novel configuration of a porous square cavity","authors":"Muhammad Faisal ,&nbsp;Talha Anwar ,&nbsp;Farah Javed","doi":"10.1016/j.padiff.2025.101315","DOIUrl":"10.1016/j.padiff.2025.101315","url":null,"abstract":"<div><div>Efficient thermal management is vital in modern mechanical and energy systems, where conventional engine oils often exhibit limited heat transfer capabilities. This study investigates the enhancement of thermal convection in engine oil by dispersing molybdenum tetrasulfide nanoparticles (MoS₄) to form a high-performance nanofluid. The natural convection behavior of this nanofluid is analyzed within a square porous cavity featuring uniformly heated horizontal walls and isothermally cooled vertical walls. The governing equations are developed using scaling variables and the Boussinesq approximation and solved numerically through the finite element method. The effects of nanoparticle volume fraction (0–0.07), Rayleigh number (10³–10⁶), and Darcy number (10⁻⁵–10⁻²) are systematically examined. Results show that increasing the MoS₄ nanoparticle concentration substantially enhances convective heat transfer, with the average Nusselt number rising by up to 28 % and the peak stream function reaching 17.0 at a volume fraction of 0.07 under low Darcy and Rayleigh conditions. These findings demonstrate that even minimal nanoparticle addition can significantly improve the heat transport capability of engine oils in porous enclosures. The study introduces a novel combination of molybdenum tetrasulfide-based nanofluids and porous media analysis, extending beyond prior work by quantifying the coupled effects of nanoparticle concentration and porous resistance on buoyancy-driven flow performance.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101315"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362459","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}

{"title":"Traveling synchronized asymmetric two-waves in the propagation of the KdV and mKdV equations incorporating time-space dispersion terms","authors":"Marwan Alquran,&nbsp;Imad Jaradat","doi":"10.1016/j.padiff.2025.101319","DOIUrl":"10.1016/j.padiff.2025.101319","url":null,"abstract":"<div><div>Joseph and Egri revised the standard Korteweg-de Vries equation by replacing its third-order space dispersion term by space-time dispersions aiming to adjust the wave speed and preserve frequency stability. The aim of the current study is twofold. First, it demonstrates that the Joseph-Egri equation exhibits dynamical behavior similar to the Boussinesq model, particularly in the propagation of synchronized asymmetric two-wave structures. Second, it presents and investigates a modified extension of the Joseph-Egri equation, inspired by similar modifications of the Korteweg-de Vries and Benjamin-Bona-Mahony equations. Effective schemes, including the trigonometric and hyperbolic rational functions method and the extended tanh-coth expansion method, are implemented to extract diverse explicit solutions for both models. These analytical results are further supported by 2D and 3D plots. The obtained findings reveal distinct physical structures for the Joseph-Egri and its modified counterparts. Specifically, the Joseph-Egri equation supports cusp soliton, bell-shaped soliton, and periodic concave-pattern solutions, while the modified Joseph-Egri equation admits kink soliton, periodic kink-pattern, and periodic concave-convex wave solutions. We believe the reported results will contribute to a deeper understanding of the synchronized propagation of bidirectional waves in various nonlinear media and related physical applications.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101319"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466069","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}