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

Retraction Notice to “Stochastic Reynolds Equation for Magnetohydrodynamics Micropolar Fluid and Surface Roughness in Squeeze-Film Lubrication Characteristics of Rough Parallel Rectangular Plates” [Partial Differential Equations in Applied Mathematics 15 (2025) 101269] 关于“粗糙平行矩形板挤压膜润滑特性中磁流体动力学微极流体和表面粗糙度的随机Reynolds方程”的撤回通知[应用数学偏微分方程15 (2025)101269]

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2026-03-06 DOI: 10.1016/j.padiff.2026.101351

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

引用次数: 0

Effects of diffusion on the tumour regression in exposure to the non-ionizing electromagnetic waves 非电离电磁波照射下扩散对肿瘤消退的影响

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2026-02-02 DOI: 10.1016/j.padiff.2026.101342

Fatemeh Ansarizadeh , Tonghua Zhang

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Modeling lump and soliton wave interactions in the (3 + 1)D Fornberg-Whitham equation using a physics-informed neural network framework 利用物理信息神经网络框架模拟（3 + 1）D Fornberg-Whitham方程中的块状波和孤子波相互作用

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2025-12-11 DOI: 10.1016/j.padiff.2025.101330

Md. Towhiduzzaman , Md. Abdul Al Mohit , A.Z.M. Asaduzzaman

{"title":"Modeling lump and soliton wave interactions in the (3 + 1)D Fornberg-Whitham equation using a physics-informed neural network framework","authors":"Md. Towhiduzzaman , Md. Abdul Al Mohit , A.Z.M. Asaduzzaman","doi":"10.1016/j.padiff.2025.101330","DOIUrl":"10.1016/j.padiff.2025.101330","url":null,"abstract":"<div><div>This paper presents an in-depth analytical and computational study of the (3 + 1)-dimensional Fornberg-Whitham (FW) equation, a highly nonlinear partial differential equation modeling complex wave interactions in multidimensional dispersive media. Employing Hirota’s bilinear method, we derive explicit lump and multi-soliton solutions, elucidating their dynamic interaction patterns and stability properties. To complement these findings, we develop a robust physics-informed neural network (PINN) framework to numerically solve the FW equation, capturing challenging rogue and breather wave phenomena with high accuracy. Comprehensive numerical experiments validate the PINN model against analytical benchmarks, demonstrating its capability to handle high-dimensional nonlinearities and mixed derivatives. These results provide critical insights into multidimensional wave dynamics and establish a hybrid approach that effectively blends classical soliton theory with modern machine learning, paving the way for future research in nonlinear wave propagation, fluid dynamics, and applied physics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101330"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792019","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}

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Comment on the paper “Sk Enamul, Seetalsmita Samal, Surender Ontela, Partial Differential Equations in Applied Mathematics 13 (2025) 101,073” 对论文“Sk Enamul, Seetalsmita Samal, Surender Ontela，应用数学中的偏微分方程13(2025)101,073”的评论

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2026-02-20 DOI: 10.1016/j.padiff.2026.101353

Asterios Pantokratoras

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Spectral numerical method for fractional order partial differential equations using Katugampola derivative 分数阶偏微分方程的卡图甘坡拉导数谱数值解法

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2026-01-25 DOI: 10.1016/j.padiff.2026.101338

Kamal Shah , Thabet Abdeljawad , Nabil Mlaiki , Hussam Alrabaiah

{"title":"Spectral numerical method for fractional order partial differential equations using Katugampola derivative","authors":"Kamal Shah , Thabet Abdeljawad , Nabil Mlaiki , Hussam Alrabaiah","doi":"10.1016/j.padiff.2026.101338","DOIUrl":"10.1016/j.padiff.2026.101338","url":null,"abstract":"<div><div>In this paper, we investigate the Telegraph fractional partial differential equations (FPDEs) with Katugampola derivative. The said derivative is a generalized form of traditional fractional order derivative. Since, for every FPDEs to find exact solution is very difficult task, therefore researchers have introduced various numerical techniques. Spectral methods based on polynomials have also considered in the last few decades very well to compute the numerical solutions for large numbers of problems of fractional order. We use shifted Jacobi polynomials to compute some numerical results for the considered class of FPDEs using Katugampola type differentiation. The adopted method is a powerful tool as needs no discretization or collocation of data. Some operational matrices are constructed on using the said polynomials to convert the considered problem to some algebraic equations. Then on using the Matlab, we present the results graphically using various fractional orders values. Some numerical examples are given to demonstrate our results.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101338"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146189147","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

Fractional mathematical modeling on monkeypox using the Laplace-Adomian decomposition method 用Laplace-Adomian分解法建立猴痘的分数数学模型

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2025-12-09 DOI: 10.1016/j.padiff.2025.101326

Sharmin Sultana Shanta , M. Ali Akbar

{"title":"Fractional mathematical modeling on monkeypox using the Laplace-Adomian decomposition method","authors":"Sharmin Sultana Shanta , M. Ali Akbar","doi":"10.1016/j.padiff.2025.101326","DOIUrl":"10.1016/j.padiff.2025.101326","url":null,"abstract":"<div><div>The monkeypox virus has become a major global health concern due to its rapid spread. Medical intervention and isolation are essential to control the outbreak until an effective treatment is discovered. In this article, we develop a fractional SEIQR model to study the transmission dynamic of the monkeypox virus by including key epidemiological factors and memory effects. The nonlinear model describing the spread of viruses is investigated using the fractional Laplace-Adomian decomposition method (LADM), a powerful analytical technique to address complex infectious disease models. The results are strictly validated by comparing them with those derived from the fractional fourth-order Runge-Kutta (RK4) method. The results demonstrate strong agreement for <span><math><mrow><mi>ζ</mi><mo>=</mo><mn>0.99</mn></mrow></math></span>, which confirms the reliability of the fractional framework. The error analysis shows that adding more LADM terms increases the accuracy. Positivity and sensitivity analyses confirm the model is biologically valid and show that early detection, isolation, quarantine, and reduced contact strongly affect infection levels. The phase portraits and contour plots provide insight into system behavior and threshold conditions. The study highlights the effectiveness of fractional LADM in describing nonlocal and memory-driven dynamics that cannot be represented in classical models.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101326"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145760655","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

Retraction Notice to “A Study on Intuitionistic Fuzzy Neutral Functional Integro-Differential PDEs with Impulses” [Partial Differential Equations in Applied Mathematics 15 (2025) 101296] “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”的撤回通知[应用数学偏微分方程15 (2025)101296]

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2026-03-06 DOI: 10.1016/j.padiff.2026.101352

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

引用次数: 0

Invariance and solitons analyses of wave equations with fourth order dispersion 四阶色散波动方程的不变性和孤子分析

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2025-12-15 DOI: 10.1016/j.padiff.2025.101327

Ali Raza , F.M. Mahomed , F.D. Zaman , A.H. Kara

引用次数: 0

Characteristics of stephan blowing and thermal radiation on williamson nanofluid with thermal non-equilibrium effect using bayesian-regularization optimizer-deep neural network 利用贝叶斯-正则化优化器-深度神经网络研究具有热非平衡效应的williamson纳米流体的斯蒂芬吹气和热辐射特性

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2026-01-27 DOI: 10.1016/j.padiff.2026.101337

Mostafa Mohamed Okasha , Munawar Abbas , Adnan Burhan Rajab , Dilsora Abduvalieva , Wei Sin Koh , Ilyas Khan , Humaira Kanwal , Ansar Abbas

{"title":"Characteristics of stephan blowing and thermal radiation on williamson nanofluid with thermal non-equilibrium effect using bayesian-regularization optimizer-deep neural network","authors":"Mostafa Mohamed Okasha , Munawar Abbas , Adnan Burhan Rajab , Dilsora Abduvalieva , Wei Sin Koh , Ilyas Khan , Humaira Kanwal , Ansar Abbas","doi":"10.1016/j.padiff.2026.101337","DOIUrl":"10.1016/j.padiff.2026.101337","url":null,"abstract":"<div><div>The purpose of this examination is to assess the effect of Stephan blowing and thermal radiation on chemical reactive flow of Williamson nanofluid flow across a sheet with Marangoni convection. Rapid advancements in technology have led to tremendous growth in the domains of machine learning and artificial intelligence. In order to solve the mathematical formulation including heat sources and chemical reactive flow using the Bayesian-Regularization approach, this study creates a machine learning model based on ANN (artificial neural networks). With error estimates of 2.51 × 10⁻¹², 1.51 × 10⁻¹², and 7.41 × 10⁻¹³ across all three scenarios, the model achieves remarkable test performance by utilizing the BRO-DNN (Bayesian-Regularization Optimizer-Deep Neural Network), exhibiting great accuracy and dependability. Numerous industrial and technical domains where heat and mass movement are important have substantial uses for the suggested paradigm. Williamson nanofluid dynamics' incorporation of Stefan blowing and thermal radiation effects is very helpful for improving heating and cooling systems, such as those used in sophisticated industrial processes, thermal energy storage, and electronic device cooling. In applications involving porous media and composite materials, the thermal non-equilibrium approach improves forecast accuracy. The precision of numerical solutions is also increased by combining the Bayesian-Regularization Optimizer with a Deep Neural Network, which makes it advantageous for machine learning-based predictive modelling in biomedical applications, aerospace thermal management, and renewable energy systems like solar collectors.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101337"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146189145","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

Boundary element method for Laplace equation in a ring domain 环域拉普拉斯方程的边界元法

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2025-12-13 DOI: 10.1016/j.padiff.2025.101334

Laurent Tchoualag , Lionel Ouya Ndjansi , Jean Daniel Mukam , Antoine Tambue

引用次数: 0