The Benjamin-Bhona-Mahony equation is a non-linear partial differential equation arising in the study of waves, oceanography, Plasma physics, and shallow water theory. In the present work, we looked at the approximate solution of non-linear Benjamin-Bona-Mahony (BBM) problem by the Optimal Homotopy Asymptotic Method with Daftardar Jeffery Polynomials (OHAM-DJ). The BBM result is compared to analytic evaluation, the Homotopy Perturbation Technique (HPM), the Adomian Decomposition Method (ADM), and the Optimal Homotopy Asymptotic Method (OHAM-DJ). Figures of precise versus approximate solutions are also created, and it is established that OHAM-DJ's solution is substantially closer to the approximative than the precise. Additionally, the outcome demonstrates the effectiveness, simplicity, ease of use, and explicitness of OAM-DJ and provides a good means of controlling the convergence of approximations.
{"title":"Application of optimal homotopy asymptotic method with use of Daftardar Jeffery Polynomials to Benjamin-Bona-Mahony equation","authors":"Showkat Ahmad Lone , Rawan Bossly , M.M. Seada , Anwar Saeed","doi":"10.1016/j.padiff.2025.101282","DOIUrl":"10.1016/j.padiff.2025.101282","url":null,"abstract":"<div><div>The Benjamin-Bhona-Mahony equation is a non-linear partial differential equation arising in the study of waves, oceanography, Plasma physics, and shallow water theory. In the present work, we looked at the approximate solution of non-linear Benjamin-Bona-Mahony (BBM) problem by the Optimal Homotopy Asymptotic Method with Daftardar Jeffery Polynomials (OHAM-DJ). The BBM result is compared to analytic evaluation, the Homotopy Perturbation Technique (HPM), the Adomian Decomposition Method (ADM), and the Optimal Homotopy Asymptotic Method (OHAM-DJ). Figures of precise versus approximate solutions are also created, and it is established that OHAM-DJ's solution is substantially closer to the approximative than the precise. Additionally, the outcome demonstrates the effectiveness, simplicity, ease of use, and explicitness of OAM-DJ and provides a good means of controlling the convergence of approximations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101282"},"PeriodicalIF":0.0,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144917795","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 : 2025-08-22DOI: 10.1016/j.padiff.2025.101291
Pramod S , Sujatha N , Sreekala C. K , Hanumagowda B. N , Kiran S , Jagadish V. Tawade , Manish Gupta , Barno Abdullaeva , M. Ijaz Khan
This research paper comprehensively investigates magnetohydrodynamic free convection in a ferrofluid-filled rectangular cavity. The researchers designed a rectangular cavity where the left vertical wall maintains a warmer temperature than the right, while the horizontal walls (top and bottom) are adiabatic. A uniform magnetic field is imposed horizontally along the positive x-axis. The main objective is to analyse the impacts of various parameters, such as Hartmann number (0 ≤ Ha ≤ 60), Rayleigh number (103 ≤ Ra ≤ 106), and volume fraction (0 ≤ ϕ ≤ 0.04), on the heat transfer characteristics and fluid flow behavior within the enclosure. The governing equations are rigorously solved using the Galerkin finite element method. Quality plots like streamlines and isotherms and quantity plots like average Nusselt number (Nua) are presented to elucidate the underlying physics. The findings indicate that increasing Rayleigh numbers increases the convective flow, whereas increasing Hartmann numbers decreases the convective flow, promoting conduction as the primary mode of heat transfer. It is also notable that the inclusion of a magnetic field significantly alters the flow and temperature distributions, leading to a notable reduction in average Nusselt number. Furthermore, the incorporation of nanoparticles is found to intensify the heat transfer rates, with higher volume fractions yielding greater thermal performance. These findings offer significant implications for advancing thermal management, material processing techniques, and magnetohydrodynamic power generation, thereby providing innovative heat transfer solutions across diverse engineering applications.
{"title":"Magnetically driven free convection of nanofluids in rectangular cavities: A FEM approach","authors":"Pramod S , Sujatha N , Sreekala C. K , Hanumagowda B. N , Kiran S , Jagadish V. Tawade , Manish Gupta , Barno Abdullaeva , M. Ijaz Khan","doi":"10.1016/j.padiff.2025.101291","DOIUrl":"10.1016/j.padiff.2025.101291","url":null,"abstract":"<div><div>This research paper comprehensively investigates magnetohydrodynamic free convection in a ferrofluid-filled rectangular cavity. The researchers designed a rectangular cavity where the left vertical wall maintains a warmer temperature than the right, while the horizontal walls (top and bottom) are adiabatic. A uniform magnetic field is imposed horizontally along the positive <em>x-</em>axis. The main objective is to analyse the impacts of various parameters, such as Hartmann number (0 ≤ <em>Ha</em> ≤ 60), Rayleigh number (10<sup>3</sup> ≤ <em>Ra</em> ≤ 10<sup>6</sup>), and volume fraction (0 ≤ ϕ ≤ 0.04), on the heat transfer characteristics and fluid flow behavior within the enclosure. The governing equations are rigorously solved using the Galerkin finite element method. Quality plots like streamlines and isotherms and quantity plots like average Nusselt number (<em>Nu<sub>a</sub></em>) are presented to elucidate the underlying physics. The findings indicate that increasing Rayleigh numbers increases the convective flow, whereas increasing Hartmann numbers decreases the convective flow, promoting conduction as the primary mode of heat transfer. It is also notable that the inclusion of a magnetic field significantly alters the flow and temperature distributions, leading to a notable reduction in average Nusselt number. Furthermore, the incorporation of nanoparticles is found to intensify the heat transfer rates, with higher volume fractions yielding greater thermal performance. These findings offer significant implications for advancing thermal management, material processing techniques, and magnetohydrodynamic power generation, thereby providing innovative heat transfer solutions across diverse engineering applications.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101291"},"PeriodicalIF":0.0,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902467","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 : 2025-08-21DOI: 10.1016/j.padiff.2025.101274
Sharanayya Swami , Ali B M Ali , Suresh Biradar , Jagadish V Tawade , M. Ijaz Khan , Nitiraj Kulkarni , Dilsora Abduvalieva , M. Waqas
This study investigates mixed convection magnetohydrodynamic (MHD) flow and heat transfer of a /water hybrid nanofluid over stretching and shrinking surfaces embedded in a porous medium, incorporating the simultaneous effects of suction/injection, thermal slip, viscous dissipation, Joule heating, and thermal radiation. The governing boundary layer equations were transformed using similarity variables and solved numerically with the MATLAB bvp4c solver, employing experimentally validated thermophysical property correlations. Parametric analysis reveals that suction enhances heat transfer by thinning the momentum and thermal boundary layers, while injection reduces it. Magnetic fields and higher nanoparticle loadings increase fluid temperature but reduce the Nusselt number. Thermal slip improves wall heat transfer, whereas viscous dissipation, Joule heating, and radiation diminish it by thickening the thermal layer. Higher Prandtl numbers yield thinner thermal boundary layers and greater heat transfer efficiency. The findings provide useful design insights for thermal systems employing hybrid nanofluids in porous and magnetically influenced environments.
{"title":"Thermal and flow characteristics of hybrid nanofluids in free-forced convection under suction/blowing effects","authors":"Sharanayya Swami , Ali B M Ali , Suresh Biradar , Jagadish V Tawade , M. Ijaz Khan , Nitiraj Kulkarni , Dilsora Abduvalieva , M. Waqas","doi":"10.1016/j.padiff.2025.101274","DOIUrl":"10.1016/j.padiff.2025.101274","url":null,"abstract":"<div><div>This study investigates mixed convection magnetohydrodynamic (MHD) flow and heat transfer of a <span><math><mrow><mi>A</mi><msub><mi>l</mi><mn>2</mn></msub><msub><mi>O</mi><mn>3</mn></msub><mo>−</mo><mo>−</mo><mi>C</mi><mi>u</mi></mrow></math></span>/water hybrid nanofluid over stretching and shrinking surfaces embedded in a porous medium, incorporating the simultaneous effects of suction/injection, thermal slip, viscous dissipation, Joule heating, and thermal radiation. The governing boundary layer equations were transformed using similarity variables and solved numerically with the MATLAB <em>bvp4c</em> solver, employing experimentally validated thermophysical property correlations. Parametric analysis reveals that suction enhances heat transfer by thinning the momentum and thermal boundary layers, while injection reduces it. Magnetic fields and higher nanoparticle loadings increase fluid temperature but reduce the Nusselt number. Thermal slip improves wall heat transfer, whereas viscous dissipation, Joule heating, and radiation diminish it by thickening the thermal layer. Higher Prandtl numbers yield thinner thermal boundary layers and greater heat transfer efficiency. The findings provide useful design insights for thermal systems employing hybrid nanofluids in porous and magnetically influenced environments.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101274"},"PeriodicalIF":0.0,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144907256","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 : 2025-08-21DOI: 10.1016/j.padiff.2025.101279
S.R. Mishra , Rupa Baithalu , P.K. Pattnaik , Subhajit Panda
The present analysis pursuit of optimizing heat transfer rate by employing a Box-Behnken machine learning design of aluminium alloy aqueous hybrid nanomaterial over a Riga Wedge surface. The interaction of alloy nanoparticles AA7072 and AA7075 are taking part in pursuing the heat flow rate of the hybrid nanomaterial in association with the radiating heat and substantial heat supplier/absorption. The heightened thermal conductivity and stability of the hybrid nanomaterial offered by the inclusion of both alloy nanoparticles address the limitations of conventional fluid. The proposed mathematical framework is converted into dimensionless form by the adequate similarity function and a computational technique is adopted for the solution of the problem. Further, a robust statistical approach such as Box-Behnken design is utilized to evaluate systematically the influence of various factors such as particle concentrations, and radiating heat. By the use of machine learning techniques, it predicts the optimal conditions for heat transfer rate. Sensitivity evaluation is conducted to assess the influence of each of the terms on the thermal performance. This ongoing investigation is utilized in several applications spanning industries for efficient thermal management including aerospace, electronics, etc. However, the important outcomes of the study are; the thinner in momentum bounding surface is observed for the enhanced Hartmann number which enhances the profile in magnitude. Further, the inclusion of heat source overshoots the heat transport properties.
{"title":"Box-Behnken design for the machine learning prediction of heat flow rate on the flow of Aluminium alloy aqueous hybrid nanomaterial over wedged Riga surface: Sensitivity analysis","authors":"S.R. Mishra , Rupa Baithalu , P.K. Pattnaik , Subhajit Panda","doi":"10.1016/j.padiff.2025.101279","DOIUrl":"10.1016/j.padiff.2025.101279","url":null,"abstract":"<div><div>The present analysis pursuit of optimizing heat transfer rate by employing a Box-Behnken machine learning design of aluminium alloy aqueous hybrid nanomaterial over a Riga Wedge surface. The interaction of alloy nanoparticles <em>AA7072</em> and <em>AA7075</em> are taking part in pursuing the heat flow rate of the hybrid nanomaterial in association with the radiating heat and substantial heat supplier/absorption. The heightened thermal conductivity and stability of the hybrid nanomaterial offered by the inclusion of both alloy nanoparticles address the limitations of conventional fluid. The proposed mathematical framework is converted into dimensionless form by the adequate similarity function and a computational technique is adopted for the solution of the problem. Further, a robust statistical approach such as Box-Behnken design is utilized to evaluate systematically the influence of various factors such as particle concentrations, and radiating heat. By the use of machine learning techniques, it predicts the optimal conditions for heat transfer rate. Sensitivity evaluation is conducted to assess the influence of each of the terms on the thermal performance. This ongoing investigation is utilized in several applications spanning industries for efficient thermal management including aerospace, electronics, etc. However, the important outcomes of the study are; the thinner in momentum bounding surface is observed for the enhanced Hartmann number which enhances the profile in magnitude. Further, the inclusion of heat source overshoots the heat transport properties.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101279"},"PeriodicalIF":0.0,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914035","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 : 2025-08-11DOI: 10.1016/j.padiff.2025.101270
Youness Saoudi , Khalid Jeaab , Hanaa Hachimi
This paper examines and applies the Monte Carlo approach to the two-dimensional Black–Scholes partial differential equation, including the Cholesky decomposition to generate correlated Brownian motions to evaluate options on two underlying assets. This study focuses on assessing the performance and risk management of investment portfolios that include these two assets, which are part of the NASDAQ 100 stock index and two active stocks of the S&P500 stock index, namely NVIDIA Corp, Tesla Inc, Apple Inc, and Microsoft Corp over one year from November 30, 2023, to November 30, 2024. The two-dimensional Black–Scholes model is chosen for its ability to capture complex market dynamics involving correlated assets. To optimize the valuation of the basket option (Call - Put), variance minimization techniques, namely control variate and stratified sampling methods, were used. The results highlight how these techniques accurately filter Brownian paths and clarify the impact of as set correlations on market behavior.
{"title":"Pricing basket options using Monte Carlo simulation employing Cholesky decomposition and variance reduction techniques under the 2D stochastic Black–Scholes equation","authors":"Youness Saoudi , Khalid Jeaab , Hanaa Hachimi","doi":"10.1016/j.padiff.2025.101270","DOIUrl":"10.1016/j.padiff.2025.101270","url":null,"abstract":"<div><div>This paper examines and applies the Monte Carlo approach to the two-dimensional Black–Scholes partial differential equation, including the Cholesky decomposition to generate correlated Brownian motions to evaluate options on two underlying assets. This study focuses on assessing the performance and risk management of investment portfolios that include these two assets, which are part of the NASDAQ 100 stock index and two active stocks of the S&P500 stock index, namely NVIDIA Corp, Tesla Inc, Apple Inc, and Microsoft Corp over one year from November 30, 2023, to November 30, 2024. The two-dimensional Black–Scholes model is chosen for its ability to capture complex market dynamics involving correlated assets. To optimize the valuation of the basket option (Call - Put), variance minimization techniques, namely control variate and stratified sampling methods, were used. The results highlight how these techniques accurately filter Brownian paths and clarify the impact of as set correlations on market behavior.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101270"},"PeriodicalIF":0.0,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144826864","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}
This study presents a comprehensive theoretical investigation into the influence of surface roughness, magnetohydrodynamics (MHD), and micropolar fluid dynamics on the squeeze film behavior between two wide, parallel rectangular plates. A modified Reynolds equation is derived by incorporating Eringen’s microcontinuum theory, Christensen’s stochastic surface roughness model, and classical hydrodynamic principles. The model accounts for the effects of a perpendicular magnetic field and longitudinal surface irregularities. Key performance parameters—namely pressure distribution, load-carrying capacity, and squeeze film duration—are obtained analytically and evaluated using dimensionless groups such as the Hartmann number, coupling number, fluid gap interaction number, and surface roughness parameter. The results demonstrate that incorporating micropolar fluid properties and MHD effects significantly enhances squeeze film performance compared to the Newtonian fluid case. Surface roughness is also found to play a beneficial role in improving load support and film retention. The findings offer valuable insights for designing advanced lubrication systems in engineering applications where microstructural effects and magnetic fields are present.
{"title":"Stochastic reynolds equation for magnetohydrodynamics micropolar fluid and surface roughness in squeeze-film lubrication characteristics of rough parallel rectangular plates","authors":"B.S. Asha , H.M. Shivakumar , B.N. Hanumagowda , Jagadish V. Tawade , Barno Abdullaeva , Manish Gupta , Murali Gundagani , Taoufik Saidani , Nadia Batool","doi":"10.1016/j.padiff.2025.101269","DOIUrl":"10.1016/j.padiff.2025.101269","url":null,"abstract":"<div><div>This study presents a comprehensive theoretical investigation into the influence of surface roughness, magnetohydrodynamics (MHD), and micropolar fluid dynamics on the squeeze film behavior between two wide, parallel rectangular plates. A modified Reynolds equation is derived by incorporating Eringen’s microcontinuum theory, Christensen’s stochastic surface roughness model, and classical hydrodynamic principles. The model accounts for the effects of a perpendicular magnetic field and longitudinal surface irregularities. Key performance parameters—namely pressure distribution, load-carrying capacity, and squeeze film duration—are obtained analytically and evaluated using dimensionless groups such as the Hartmann number, coupling number, fluid gap interaction number, and surface roughness parameter. The results demonstrate that incorporating micropolar fluid properties and MHD effects significantly enhances squeeze film performance compared to the Newtonian fluid case. Surface roughness is also found to play a beneficial role in improving load support and film retention. The findings offer valuable insights for designing advanced lubrication systems in engineering applications where microstructural effects and magnetic fields are present.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101269"},"PeriodicalIF":0.0,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830958","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 : 2025-07-29DOI: 10.1016/j.padiff.2025.101261
Abderrahim El Ayboudi , Radoine Belkanoufi , Abdelkarim Hajjaj
This paper investigates the indirect boundary observability properties of one-dimensional strongly coupled wave equations in an approximated setting. Classical numerical discretization methods, such as finite differences and finite elements, typically fail to maintain uniform observability inequalities when applied to wave systems. This failure is primarily attributed to the emergence of high-frequency numerical solutions. The present work demonstrates a different approach through the implementation of these discretization schemes on a carefully designed non-uniform mesh. This study successfully establishes uniform observability inequalities for the coupled system. This methodology effectively recovers the system’s total energy through boundary observations, overcoming the well-documented limitations of traditional numerical approaches in wave equation systems.
{"title":"Uniform indirect boundary observability for a spatial discretization of strongly coupled wave equations","authors":"Abderrahim El Ayboudi , Radoine Belkanoufi , Abdelkarim Hajjaj","doi":"10.1016/j.padiff.2025.101261","DOIUrl":"10.1016/j.padiff.2025.101261","url":null,"abstract":"<div><div>This paper investigates the indirect boundary observability properties of one-dimensional strongly coupled wave equations in an approximated setting. Classical numerical discretization methods, such as finite differences and finite elements, typically fail to maintain uniform observability inequalities when applied to wave systems. This failure is primarily attributed to the emergence of high-frequency numerical solutions. The present work demonstrates a different approach through the implementation of these discretization schemes on a carefully designed non-uniform mesh. This study successfully establishes uniform observability inequalities for the coupled system. This methodology effectively recovers the system’s total energy through boundary observations, overcoming the well-documented limitations of traditional numerical approaches in wave equation systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101261"},"PeriodicalIF":0.0,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144772096","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 : 2025-07-28DOI: 10.1016/j.padiff.2025.101257
Thokozani Blessing Shiba, Khadijo Rashid Adem
This study examines the Camassa–Holm–Kadomtsev–Petviashvili equation with power law nonlinearity in (3+1)-D. The highlighted equation appears in mathematical physics, particularly in the study of nonlinear optics, plasma, integrable systems, and soliton theory, among other areas. The integration of the underlying equation is done using Lie symmetry analysis. To get more precise answers, the ansatz approach is applied. Traveling wave solutions are then obtained. The multiplier approach will be used to obtain conservation laws for the underlying equation.
{"title":"On the exact explicit solutions and conservation laws of the generalized (3+1)-D Camassa–Holm–Kadomtsev–Petviashvili equation with power law nonlinearity","authors":"Thokozani Blessing Shiba, Khadijo Rashid Adem","doi":"10.1016/j.padiff.2025.101257","DOIUrl":"10.1016/j.padiff.2025.101257","url":null,"abstract":"<div><div>This study examines the Camassa–Holm–Kadomtsev–Petviashvili equation with power law nonlinearity in (3+1)-D. The highlighted equation appears in mathematical physics, particularly in the study of nonlinear optics, plasma, integrable systems, and soliton theory, among other areas. The integration of the underlying equation is done using Lie symmetry analysis. To get more precise answers, the ansatz approach is applied. Traveling wave solutions are then obtained. The multiplier approach will be used to obtain conservation laws for the underlying equation.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101257"},"PeriodicalIF":0.0,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144779770","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 : 2025-07-26DOI: 10.1016/j.padiff.2025.101264
Ali Ahadi , Seyed Mostafa Mousavi , Amir Mohammad Alinia , Hossein Khademi
Partial differential equations (PDEs), particularly those involving fractional derivatives, have garnered considerable attention due to their ability to model complex systems with memory and hereditary properties. This paper focuses on the generalized Caputo fractional equation and presents a comparative analysis of three powerful solution techniques: the Homotopy Perturbation Method (HPM), the Variational Iteration Method (VIM), and the Akbari-Ganji Method (AGM). These methods are applied to fractional differential equations (FDEs) to derive approximate solutions. The accuracy and effectiveness of the methods are demonstrated through detailed comparisons with exact solutions and previous works in the field.
The study highlights the strengths of each technique in handling non-linear and fractional-order problems, providing reliable results with minimal error. Specifically, the HPM and VIM show remarkable convergence properties, while the AGM proves efficient in solving both linear and non-linear equations. These methods are validated by comparing the results with known solutions, which shows that these techniques work for a wide range of FDEs. The present study underscores the applicability of these approaches in several scientific and technological domains, hence promoting more advancements in the numerical examination of fractional systems.
{"title":"Analytical simulation of the nonlinear Caputo fractional equations","authors":"Ali Ahadi , Seyed Mostafa Mousavi , Amir Mohammad Alinia , Hossein Khademi","doi":"10.1016/j.padiff.2025.101264","DOIUrl":"10.1016/j.padiff.2025.101264","url":null,"abstract":"<div><div>Partial differential equations (PDEs), particularly those involving fractional derivatives, have garnered considerable attention due to their ability to model complex systems with memory and hereditary properties. This paper focuses on the generalized Caputo fractional equation and presents a comparative analysis of three powerful solution techniques: the Homotopy Perturbation Method (HPM), the Variational Iteration Method (VIM), and the Akbari-Ganji Method (AGM). These methods are applied to fractional differential equations (FDEs) to derive approximate solutions. The accuracy and effectiveness of the methods are demonstrated through detailed comparisons with exact solutions and previous works in the field.</div><div>The study highlights the strengths of each technique in handling non-linear and fractional-order problems, providing reliable results with minimal error. Specifically, the HPM and VIM show remarkable convergence properties, while the AGM proves efficient in solving both linear and non-linear equations. These methods are validated by comparing the results with known solutions, which shows that these techniques work for a wide range of FDEs. The present study underscores the applicability of these approaches in several scientific and technological domains, hence promoting more advancements in the numerical examination of fractional systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101264"},"PeriodicalIF":0.0,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724410","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 : 2025-07-25DOI: 10.1016/j.padiff.2025.101263
P. Kumar , AR. Ajaykumar , F. Almeida , S. Saranya , Qasem Al-Mdallal
Statistical and numerical approach is provided in the current article for Casson-Carreau nanofluid transient flow over continuously elongated sheet of curved feature. The flow is subjected under the various generation, Joule heating, non-linear thermal radiation, activation energy, second order slip, and convective peripheral conditions. Identifying the parameters that optimize the heat transfer rate and using those parameters applying the appropriate statistical tool to optimize the heat transfer rate are the two motives behind this study. A regression analysis is executed on the entropy generated; it has analyzed statistically using response surface methodology. For the issue under consideration, a Runge-Kutta-Fehlberg 4–5th order scheme has been implemented. Here, the study shows that although the Darcy number and first order slip decelerates velocity, the second order slip improves the velocity regime. Additionally, the study has showed that the activation energy parameter leverages the same, while chemical reaction parameter has negative effect on mass dispersion. With an increase in Brinkmann number, entropy production likewise rises, and fluid friction irreversibilities become more prevalent. As unsteadiness and activation energy parameters increase, Sherwood number declines. The visual representation of isotherms and streamlines is presented to display the flow and temperature pattern as a summary of the study. For the experimental setup by RSM, the better correlation coefficient is 99.93 % attained. The Pareto-chart specifies 2.2 to be the vital point for the statistical experimental design considered. For all the levels of heat source parameter and Eckert number, Radiation parameter exhibits positive sensitivity.
{"title":"Statistical and numerical investigation of irreversibility for time-dependent Casson-Carreau nanofluid flow driven by curved surface: Regression analysis","authors":"P. Kumar , AR. Ajaykumar , F. Almeida , S. Saranya , Qasem Al-Mdallal","doi":"10.1016/j.padiff.2025.101263","DOIUrl":"10.1016/j.padiff.2025.101263","url":null,"abstract":"<div><div>Statistical and numerical approach is provided in the current article for Casson-Carreau nanofluid transient flow over continuously elongated sheet of curved feature. The flow is subjected under the various generation, Joule heating, non-linear thermal radiation, activation energy, second order slip, and convective peripheral conditions. Identifying the parameters that optimize the heat transfer rate and using those parameters applying the appropriate statistical tool to optimize the heat transfer rate are the two motives behind this study. A regression analysis is executed on the entropy generated; it has analyzed statistically using response surface methodology. For the issue under consideration, a Runge-Kutta-Fehlberg 4–5th order scheme has been implemented. Here, the study shows that although the Darcy number and first order slip decelerates velocity, the second order slip improves the velocity regime. Additionally, the study has showed that the activation energy parameter leverages the same, while chemical reaction parameter has negative effect on mass dispersion. With an increase in Brinkmann number, entropy production likewise rises, and fluid friction irreversibilities become more prevalent. As unsteadiness and activation energy parameters increase, Sherwood number declines. The visual representation of isotherms and streamlines is presented to display the flow and temperature pattern as a summary of the study. For the experimental setup by RSM, the better correlation coefficient is 99.93 % attained. The Pareto-chart specifies 2.2 to be the vital point for the statistical experimental design considered. For all the levels of heat source parameter and Eckert number, Radiation parameter exhibits positive sensitivity.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101263"},"PeriodicalIF":0.0,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829639","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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