Partial Differential Equations in Applied Mathematics最新文献

{"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":"2025-09-29","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":"Analytic investigation of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation with M-fractional derivative","authors":"Zehra Tat,&nbsp;Emrullah Yaşar","doi":"10.1016/j.padiff.2025.101302","DOIUrl":"10.1016/j.padiff.2025.101302","url":null,"abstract":"<div><div>In this study, we examine the Heisenberg ferromagnetic spin chain equation in complex form in (2+1) dimensions, which is closely related to ferromagnetic materials and is used in spin wave dynamics modeling. To better interpret the model physically, we considered M-truncated time fractional derivative operator and used the generalized exponential rational function and extended trial equation methods to reveal the exact solution forms. These exact solution forms are presented in hyperbolic, trigonometric, and rational forms. We give 2D and 3D numerical simulations of exact solution profiles. The importance of fractional calculus in extending nonlinear theory is emphasized.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101302"},"PeriodicalIF":0.0,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221911","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":"2025-09-27","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":"New global regularity result for the 3D incompressible Navier–Stokes equations","authors":"Abdelhafid Younsi","doi":"10.1016/j.padiff.2025.101306","DOIUrl":"10.1016/j.padiff.2025.101306","url":null,"abstract":"<div><div>In this paper we establish the global existence in time of strong solutions to the 3D incompressible Navier–Stokes system for small viscosity and large initial data. The obtained result is valid in bounded domains and in the whole space. This result provides valuable insights into significant open problems in both physics and mathematics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101306"},"PeriodicalIF":0.0,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221957","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":"Dynamical wave structures for time-fractional (3+1)-dimensional p-type model via two improved techniques","authors":"Makhdoom Ali ,&nbsp;Muhammad Bilal Riaz ,&nbsp;Nauman Ahmed ,&nbsp;Muhammad Zafarullah Baber ,&nbsp;Ali Akgül","doi":"10.1016/j.padiff.2025.101303","DOIUrl":"10.1016/j.padiff.2025.101303","url":null,"abstract":"<div><div>In this work, we investigates the conformable time-fractional (3+1)-dimensional p-type model for the analytical solutions. The underlying model is explained the material characteristics and spontaneous processes in solid-state physics, such as magnetism and conventional particle physics. To obtain the analytical solutions, we used the novel Kumar–Malik method and the new extended direct algebraic method. We derived the analytical solutions through the application of the conformal fractional derivative and the fractional wave transformation. We successfully obtain several solutions in the form of rational, hyperbolic, mixed trigonometric, mixed hyperbolic, exponential, Jacobi elliptic, and trigonometric functions by using these methods. The found solutions include various solitary wave solutions as well as bright, dark, and w-shaped soliton solutions. With the use of Mathematica 13.0, the analytical soliton solutions are further shown in 3D, contour and 2D representations, assisting in the understanding of these complex wave phenomena.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101303"},"PeriodicalIF":0.0,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221967","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":"2025-09-19","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":"2025-09-15","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":"Higher dimensional nonlinear model arising to the diversity of fields: Dynamics of wave structures with M-fractional derivative","authors":"Usman Younas ,&nbsp;Jan Muhammad ,&nbsp;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":"2025-09-15","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}

{"title":"Mathematical model of immune response to Hepatitis C virus (HCV) disease","authors":"Amna H.A. Ibrahim,&nbsp;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":"2025-09-13","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}

{"title":"Numerical solution of the variable-order time fractional advection reaction–diffusion equation via combination of a Newton’s polynomial and Cubic B-spline method","authors":"A.S.V. Ravi Kanth,&nbsp;Varela Pavankalyan","doi":"10.1016/j.padiff.2025.101289","DOIUrl":"10.1016/j.padiff.2025.101289","url":null,"abstract":"<div><div>This work presents a numerical technique based on the cubic B-spline function for solving the variable-order time fractional advection reaction–diffusion equation in the sense of the Caputo derivative. Newton’s interpolation formulation has been employed to approximate the variable-order time-fractional derivative, while the cubic B-spline functions are utilized for spatial discretization. The proposed methodology demonstrated unconditionally stable and convergence of order <span><math><mrow><mo>(</mo><mi>Δ</mi><msup><mrow><mstyle><mi>r</mi></mstyle></mrow><mrow><mn>4</mn><mo>−</mo><mi>ϑ</mi><mrow><mo>(</mo><mi>ς</mi><mo>,</mo><mstyle><mi>r</mi></mstyle><mo>)</mo></mrow></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></math></span> through the Von Neumann analysis. Numerical investigations that confirm theoretical conclusions using data visualizations and tables to illustrate efficiency and accuracy. Furthermore, the comparative findings demonstrate that the novel discretization methodology outperforms the other techniques present in the literature in terms of accuracy.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101289"},"PeriodicalIF":0.0,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048528","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}