Pub Date : 2025-10-14DOI: 10.1016/j.padiff.2025.101310
Tooba Sadaf , Ali B.M. Ali , Sami Ullah Khan , M. Ijaz Khan , Nidhal Ben Khedher
This investigation explored the bioconvection applications in rotatory disk nanofluid flow with implementation of magnetic field. The heat transfer analysis involved the significance of radiated effects while chemical reactive species are utilized to the concentration equation. The investigation accounts the convective thermal constraints to analyze the heat transfer impact. The problem is simplified by using the appropriate variables and set of dimensionless equations has been obtained. For solution methodology, shooting technique is adopted. A detailed physical analysis is performed in view of modeled flow parameters. It has been observed that azimuthal velocity component increases due to ratio of stretching to rotation parameter. Change in ratio of stretching to rotation parameter enhances declines the temperature profile.
{"title":"Numerical exploration for bioconvective nanofluid flow towards a rotating surface with chemical reaction and radiative effects","authors":"Tooba Sadaf , Ali B.M. Ali , Sami Ullah Khan , M. Ijaz Khan , Nidhal Ben Khedher","doi":"10.1016/j.padiff.2025.101310","DOIUrl":"10.1016/j.padiff.2025.101310","url":null,"abstract":"<div><div>This investigation explored the bioconvection applications in rotatory disk nanofluid flow with implementation of magnetic field. The heat transfer analysis involved the significance of radiated effects while chemical reactive species are utilized to the concentration equation. The investigation accounts the convective thermal constraints to analyze the heat transfer impact. The problem is simplified by using the appropriate variables and set of dimensionless equations has been obtained. For solution methodology, shooting technique is adopted. A detailed physical analysis is performed in view of modeled flow parameters. It has been observed that azimuthal velocity component increases due to ratio of stretching to rotation parameter. Change in ratio of stretching to rotation parameter enhances declines the temperature profile.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101310"},"PeriodicalIF":0.0,"publicationDate":"2025-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362457","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}
Pub Date : 2025-10-06DOI: 10.1016/j.padiff.2025.101307
K. Rajyalakshmi, G. Ravi Kiran, N. Lavanya
This study provides an analytical examination of the hemodynamic characteristics of two-layered blood flow in a diverging narrow channel featuring multiple symmetrical stenoses, porous wall effects, and slip boundary conditions. The central region, characterized by a concentration of RBCs, is modeled as a Jeffrey fluid, whereas the peripheral region is considered Newtonian. Under the assumption of mild stenosis and incompressible, completely developed laminar movement, the governing equations are precisely formulated and solved through direct integration. Closed-form expressions for velocity, mean hematocrit, core hematocrit and effective viscosity have been obtained. Parametric analysis indicates that velocity escalates with the Jeffrey parameter and slip, whereas effective viscosity diminishes with elevated Jeffrey parameter and Darcy number values, but augments with slip and stenosis height. The core and mean hematocrit diminish with most parameter variations, yet increase with the Jeffrey parameter. These findings improve comprehension of pathological conditions such as arterial occlusions and illustrate microcirculatory effects, including the Fåhraeus–Lindqvist phenomenon. The integrated modeling framework enhances physiological relevance and facilitates biomedical applications in the diagnosis and treatment of vascular diseases.
{"title":"Hemodynamic analysis of Jeffrey blood flow with two-layered model through a multiple stenoses in a diverging narrow channel with a porous layer under slip conditions","authors":"K. Rajyalakshmi, G. Ravi Kiran, N. Lavanya","doi":"10.1016/j.padiff.2025.101307","DOIUrl":"10.1016/j.padiff.2025.101307","url":null,"abstract":"<div><div>This study provides an analytical examination of the hemodynamic characteristics of two-layered blood flow in a diverging narrow channel featuring multiple symmetrical stenoses, porous wall effects, and slip boundary conditions. The central region, characterized by a concentration of RBCs, is modeled as a Jeffrey fluid, whereas the peripheral region is considered Newtonian. Under the assumption of mild stenosis and incompressible, completely developed laminar movement, the governing equations are precisely formulated and solved through direct integration. Closed-form expressions for velocity, mean hematocrit, core hematocrit and effective viscosity have been obtained. Parametric analysis indicates that velocity escalates with the Jeffrey parameter and slip, whereas effective viscosity diminishes with elevated Jeffrey parameter and Darcy number values, but augments with slip and stenosis height. The core and mean hematocrit diminish with most parameter variations, yet increase with the Jeffrey parameter. These findings improve comprehension of pathological conditions such as arterial occlusions and illustrate microcirculatory effects, including the Fåhraeus–Lindqvist phenomenon. The integrated modeling framework enhances physiological relevance and facilitates biomedical applications in the diagnosis and treatment of vascular diseases.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101307"},"PeriodicalIF":0.0,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268619","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}
Pub Date : 2025-10-03DOI: 10.1016/j.padiff.2025.101304
Kosuke Kita , Kei Matsushima , Tomoyuki Oka
This paper is concerned with configurations of two-material thermal conductors that minimize the Dirichlet energy for steady-state diffusion equations with nonlinear boundary conditions described mainly by maximal monotone operators. To find such configurations, a homogenization theorem will be proved and applied to an existence theorem for minimizers of a relaxation problem whose minimum value is equivalent to an original design problem. As a typical example of nonlinear boundary conditions, thermal radiation boundary conditions will be the focus, and then the sensitivity of the Dirichlet energy will be derived, which is used to estimate the minimum value. Since optimal configurations of the relaxation problem involve the so-called grayscale domains that do not make sense in general, a perimeter constraint problem via the positive part of the level set function will be introduced as an approximation problem to avoid such domains, and moreover, the existence theorem for minimizers of the perimeter constraint problem will be proved. In particular, it will also be proved that the limit of minimizers for the approximation problem becomes that of the relaxation problem in a specific case, and then candidates for minimizers of the approximation problem will be constructed by employing a nonlinear diffusion-based level set method. In this paper, it will be shown that optimized configurations deeply depend on force terms as a characteristic of nonlinear problems and will also be applied to real physical problems.
{"title":"Optimal design problem with thermal radiation","authors":"Kosuke Kita , Kei Matsushima , Tomoyuki Oka","doi":"10.1016/j.padiff.2025.101304","DOIUrl":"10.1016/j.padiff.2025.101304","url":null,"abstract":"<div><div>This paper is concerned with configurations of two-material thermal conductors that minimize the Dirichlet energy for steady-state diffusion equations with nonlinear boundary conditions described mainly by maximal monotone operators. To find such configurations, a homogenization theorem will be proved and applied to an existence theorem for minimizers of a relaxation problem whose minimum value is equivalent to an original design problem. As a typical example of nonlinear boundary conditions, thermal radiation boundary conditions will be the focus, and then the sensitivity of the Dirichlet energy will be derived, which is used to estimate the minimum value. Since optimal configurations of the relaxation problem involve the so-called grayscale domains that do not make sense in general, a perimeter constraint problem via the positive part of the level set function will be introduced as an approximation problem to avoid such domains, and moreover, the existence theorem for minimizers of the perimeter constraint problem will be proved. In particular, it will also be proved that the limit of minimizers for the approximation problem becomes that of the relaxation problem in a specific case, and then candidates for minimizers of the approximation problem will be constructed by employing a nonlinear diffusion-based level set method. In this paper, it will be shown that optimized configurations deeply depend on force terms as a characteristic of nonlinear problems and will also be applied to real physical problems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101304"},"PeriodicalIF":0.0,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362460","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}
Pub Date : 2025-10-01DOI: 10.1016/j.padiff.2025.101308
Tasmia Hoque , Samir Kumar Bhowmik
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.
{"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":"2025-10-01","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}
Pub Date : 2025-09-29DOI: 10.1016/j.padiff.2025.101290
Bilal Ahmad, Muhammad Ozair Ahmed
This study presents a mathematical model to analyze heat transport in a hybrid nanofluid composed of aluminum oxide (AlO) 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 MATLAB. 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.
{"title":"Mathematical modeling for heat transportation analysis in hybrid nanofluid through a wedge surface under the influence of magnetic field","authors":"Bilal Ahmad, 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}
Pub Date : 2025-09-29DOI: 10.1016/j.padiff.2025.101302
Zehra Tat, Emrullah Yaşar
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.
{"title":"Analytic investigation of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation with M-fractional derivative","authors":"Zehra Tat, 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}
Pub Date : 2025-09-27DOI: 10.1016/j.padiff.2025.101305
Shaher Momani , Rabha W. Ibrahim
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 -fractional calculus. This calculus is based on the generalization of the quantum gamma function (). By employing -fractional derivatives in the form of the -Mittag-Leffler function, we explore the dynamics of soliton fields in these materials. The model considers key parameters such as the fractional order , the generalized parameters and , and the initial weight parameter . 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.
{"title":"Soliton propagation in optical metamaterials with nonlocal responses: A fractional calculus approach using (q,τ)-Mittag-Leffler functions","authors":"Shaher Momani , 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}
Pub Date : 2025-09-26DOI: 10.1016/j.padiff.2025.101306
Abdelhafid Younsi
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.
{"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}
Pub Date : 2025-09-23DOI: 10.1016/j.padiff.2025.101303
Makhdoom Ali , Muhammad Bilal Riaz , Nauman Ahmed , Muhammad Zafarullah Baber , Ali Akgül
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.
{"title":"Dynamical wave structures for time-fractional (3+1)-dimensional p-type model via two improved techniques","authors":"Makhdoom Ali , Muhammad Bilal Riaz , Nauman Ahmed , Muhammad Zafarullah Baber , 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}
Pub Date : 2025-09-19DOI: 10.1016/j.padiff.2025.101299
Mehari Fentahun Endalew, Xiaoming Zhang
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.
{"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, 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}
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