Pub Date : 2025-12-15DOI: 10.1016/j.padiff.2025.101327
Ali Raza , F.M. Mahomed , F.D. Zaman , A.H. Kara
We study the non-linear wave equation for arbitrary function with fourth order dispersion. A special case that is analysed exclusively is the model of nerve membranes; we consider this model, both, in the presence and absence of the fourth order dispersion. The equivalence transformations, Lie symmetries and a complete classification is presented. We also discuss the one dimensional optimal system in each case obtained via classification. The reduction of the partial differential equations (PDEs) is carried out and the forms of invariant solutions are presented. The study also include the construction of conservation laws using the direct method. The invariant solutions and some special type of solutions including solitons are presented with their graphical illustrations. we derive homoclinic breather solutions (HBs) and M-shaped rational solutions (MSRs). Their dynamic is shown in figures by selecting appropriate values of parameters.
{"title":"Invariance and solitons analyses of wave equations with fourth order dispersion","authors":"Ali Raza , F.M. Mahomed , F.D. Zaman , A.H. Kara","doi":"10.1016/j.padiff.2025.101327","DOIUrl":"10.1016/j.padiff.2025.101327","url":null,"abstract":"<div><div>We study the non-linear wave equation for arbitrary function with fourth order dispersion. A special case that is analysed exclusively is the model of nerve membranes; we consider this model, both, in the presence and absence of the fourth order dispersion. The equivalence transformations, Lie symmetries and a complete classification is presented. We also discuss the one dimensional optimal system in each case obtained via classification. The reduction of the partial differential equations (PDEs) is carried out and the forms of invariant solutions are presented. The study also include the construction of conservation laws using the direct method. The invariant solutions and some special type of solutions including solitons are presented with their graphical illustrations. we derive homoclinic breather solutions (HBs) and M-shaped rational solutions (MSRs). Their dynamic is shown in figures by selecting appropriate values of parameters.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101327"},"PeriodicalIF":0.0,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791940","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 : 2025-12-13DOI: 10.1016/j.padiff.2025.101329
Realeboga Dikole
This article investigates nonlinear Dirac equations (NLD) with cubic-type nonlinearities, that is, vector and scalar self-interaction nonlinearities. We present analytical solutions of gap-solitons, which are self-localised, moving or quiescent pulses existing in the band gaps of nonlinear Dirac models. We also perform the linear stability analysis of the gap-soliton bearing systems and find that the gap-solitons possess some regions of instability. We also extend our studies to planar nonlinear Dirac equations and relate them to light propagation in photonic lattices, such as photonic graphene and present their numerical solutions, in particular, the rotationally symmetric localised radial profiles that rotate about the Brillouin zone.
{"title":"Spinor solitons in one-dimensional and planar nonlinear Dirac equations","authors":"Realeboga Dikole","doi":"10.1016/j.padiff.2025.101329","DOIUrl":"10.1016/j.padiff.2025.101329","url":null,"abstract":"<div><div>This article investigates nonlinear Dirac equations (NLD) with cubic-type nonlinearities, that is, vector and scalar self-interaction nonlinearities. We present analytical solutions of gap-solitons, which are self-localised, moving or quiescent pulses existing in the band gaps of nonlinear Dirac models. We also perform the linear stability analysis of the gap-soliton bearing systems and find that the gap-solitons possess some regions of instability. We also extend our studies to planar nonlinear Dirac equations and relate them to light propagation in photonic lattices, such as photonic graphene and present their numerical solutions, in particular, the rotationally symmetric localised radial profiles that rotate about the Brillouin zone.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101329"},"PeriodicalIF":0.0,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791939","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 : 2025-12-13DOI: 10.1016/j.padiff.2025.101332
G. Shylaja , V. Kesavulu Naidu , B. Venkatesh , S.M. Mallikarjunaiah
This paper presents an explicit integration scheme that incorporates septic-order triangular elements. Cubic arcs are utilized to approximate the curved edges of these elements. This methodology is particularly effective for discretizing curved domains, and its primary objective is the approximation of equations involving differential operators. A 36-node septic-order triangular element with a curved boundary, which consists of one curved edge and two straight edges, is introduced in this study. This element serves as the foundation for the isoparametric coordinate transformation discussed herein. A standard triangle in the local coordinate system is mapped onto the curved triangular element in the global coordinate system by means of a unique point transformation. The curved triangular element is replaced by septic arcs, and the coordinates located on the curved edge are embedded within the parameters that define these arc equations. Each arc consistently represents a distinct cubic arc due to the relationships involved in the parameter calculations. Consequently, the overall numerical approximation is highly accurate. For higher-order curved triangular elements, the finite element method, in conjunction with numerical integration that utilizes curved boundary point transformations (applicable to both the exterior and interior of each curved triangular element), will act as a robust subparametric coordinate transformation and, as a result, a formidable numerical technique. The efficacy of this method is demonstrated through the resolution of three boundary value problems. Numerical outcomes affirm that the proposed technique significantly surpasses existing methods in the approximation of boundary value problems.
{"title":"Septic-order triangular finite elements: An explicit method with cubic arc subparametric transformations","authors":"G. Shylaja , V. Kesavulu Naidu , B. Venkatesh , S.M. Mallikarjunaiah","doi":"10.1016/j.padiff.2025.101332","DOIUrl":"10.1016/j.padiff.2025.101332","url":null,"abstract":"<div><div>This paper presents an explicit integration scheme that incorporates septic-order triangular elements. Cubic arcs are utilized to approximate the curved edges of these elements. This methodology is particularly effective for discretizing curved domains, and its primary objective is the approximation of equations involving differential operators. A 36-node septic-order triangular element with a curved boundary, which consists of one curved edge and two straight edges, is introduced in this study. This element serves as the foundation for the isoparametric coordinate transformation discussed herein. A standard triangle in the local coordinate system is mapped onto the curved triangular element in the global coordinate system by means of a unique point transformation. The curved triangular element is replaced by septic arcs, and the coordinates located on the curved edge are embedded within the parameters that define these arc equations. Each arc consistently represents a distinct cubic arc due to the relationships involved in the parameter calculations. Consequently, the overall numerical approximation is highly accurate. For higher-order curved triangular elements, the finite element method, in conjunction with numerical integration that utilizes curved boundary point transformations (applicable to both the exterior and interior of each curved triangular element), will act as a robust subparametric coordinate transformation and, as a result, a formidable numerical technique. The efficacy of this method is demonstrated through the resolution of three boundary value problems. Numerical outcomes affirm that the proposed technique significantly surpasses existing methods in the approximation of boundary value problems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101332"},"PeriodicalIF":0.0,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-12DOI: 10.1016/j.padiff.2025.101325
Dian K. Palagachev
The non-homogeneous conormal derivative problems for nonlinear, second-order divergence form elliptic equations with singular data appear naturally in mathematical modeling of real phenomena involving problems of image recovery, the thermistor problem, or studies of non-Newtonian fluids.
We prove suitable estimates for certain surface integrals, related to non-homogeneous conormal derivative problems, which lead to essential boundedness of the weak solutions under quite general hypotheses on the data.
{"title":"On certain surface integrals related to the conormal derivative problem","authors":"Dian K. Palagachev","doi":"10.1016/j.padiff.2025.101325","DOIUrl":"10.1016/j.padiff.2025.101325","url":null,"abstract":"<div><div>The non-homogeneous conormal derivative problems for nonlinear, second-order divergence form elliptic equations with singular data appear naturally in mathematical modeling of real phenomena involving problems of image recovery, the thermistor problem, or studies of non-Newtonian fluids.</div><div>We prove suitable estimates for certain surface integrals, related to non-homogeneous conormal derivative problems, which lead to essential boundedness of the weak solutions under quite general hypotheses on the data.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101325"},"PeriodicalIF":0.0,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145760656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-11DOI: 10.1016/j.padiff.2025.101333
M.M. Nour , Abdur Rehman , Abdallah aldurayhim , Muhammad Ashraf , A.M. Rashad , Hossam A. Nabwey
This study investigates the effects of non-linear motion on mixed convection viscous fluid flow, incorporating thermal conductivity inversely proportional to a linear function of temperature under the influence of oscillating thermal waves. To provide a comprehensive understanding, the research explores convective heat transfer in the presence of vorticity. The governing equations, including continuity, momentum, and heat equations, are formulated to represent the intricate non-linear dynamics of fluid flow and heat transfer. These equations are rendered dimensionless using appropriate scaling variables and subsequently transformed into steady and unsteady forms to address varying thermal and flow conditions. A Gaussian elimination approach, combined with a primitive variable formulation, is employed for numerical computation, alongside the finite difference method. Computational solutions are developed using FORTRAN Laher-90, with graphical and tabular results presented via Tecplot-360 to analyze transient shear stress (τs) and transient heat transfer (τt) influenced by oscillating thermal waves. The findings reveal critical insights into the interplay between vorticity, non-linear fluid behavior, and thermal oscillations, contributing to advancements in optimizing convective heat transfer mechanisms. The findings show that in steady-state conditions, temperature distribution and flow velocity increase with higher values of the thermal conductivity variation parameter (ς). In the unsteady state, transient shear stress τₛ exhibits higher wave amplitude at ς = 0.2, followed by slight changes in phase angle at different values. However, transient heat transfer τt decreases in wave magnitude as ς increases.
{"title":"Influence of non-linear motion on mixed convection in viscous fluids with temperature-dependent thermal conductivity and oscillating thermal wave","authors":"M.M. Nour , Abdur Rehman , Abdallah aldurayhim , Muhammad Ashraf , A.M. Rashad , Hossam A. Nabwey","doi":"10.1016/j.padiff.2025.101333","DOIUrl":"10.1016/j.padiff.2025.101333","url":null,"abstract":"<div><div>This study investigates the effects of non-linear motion on mixed convection viscous fluid flow, incorporating thermal conductivity inversely proportional to a linear function of temperature under the influence of oscillating thermal waves. To provide a comprehensive understanding, the research explores convective heat transfer in the presence of vorticity. The governing equations, including continuity, momentum, and heat equations, are formulated to represent the intricate non-linear dynamics of fluid flow and heat transfer. These equations are rendered dimensionless using appropriate scaling variables and subsequently transformed into steady and unsteady forms to address varying thermal and flow conditions. A Gaussian elimination approach, combined with a primitive variable formulation, is employed for numerical computation, alongside the finite difference method. Computational solutions are developed using FORTRAN Laher-90, with graphical and tabular results presented via Tecplot-360 to analyze transient shear stress (τ<sub><em>s</em></sub>) and transient heat transfer (τ<sub><em>t</em></sub>) influenced by oscillating thermal waves. The findings reveal critical insights into the interplay between vorticity, non-linear fluid behavior, and thermal oscillations, contributing to advancements in optimizing convective heat transfer mechanisms. The findings show that in steady-state conditions, temperature distribution and flow velocity increase with higher values of the thermal conductivity variation parameter (ς). In the unsteady state, transient shear stress τₛ exhibits higher wave amplitude at ς = 0.2, followed by slight changes in phase angle at different values. However, transient heat transfer τ<sub>t</sub> decreases in wave magnitude as ς increases.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101333"},"PeriodicalIF":0.0,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791934","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 : 2025-12-11DOI: 10.1016/j.padiff.2025.101330
Md. Towhiduzzaman , Md. Abdul Al Mohit , A.Z.M. Asaduzzaman
This paper presents an in-depth analytical and computational study of the (3 + 1)-dimensional Fornberg-Whitham (FW) equation, a highly nonlinear partial differential equation modeling complex wave interactions in multidimensional dispersive media. Employing Hirota’s bilinear method, we derive explicit lump and multi-soliton solutions, elucidating their dynamic interaction patterns and stability properties. To complement these findings, we develop a robust physics-informed neural network (PINN) framework to numerically solve the FW equation, capturing challenging rogue and breather wave phenomena with high accuracy. Comprehensive numerical experiments validate the PINN model against analytical benchmarks, demonstrating its capability to handle high-dimensional nonlinearities and mixed derivatives. These results provide critical insights into multidimensional wave dynamics and establish a hybrid approach that effectively blends classical soliton theory with modern machine learning, paving the way for future research in nonlinear wave propagation, fluid dynamics, and applied physics.
{"title":"Modeling lump and soliton wave interactions in the (3 + 1)D Fornberg-Whitham equation using a physics-informed neural network framework","authors":"Md. Towhiduzzaman , Md. Abdul Al Mohit , A.Z.M. Asaduzzaman","doi":"10.1016/j.padiff.2025.101330","DOIUrl":"10.1016/j.padiff.2025.101330","url":null,"abstract":"<div><div>This paper presents an in-depth analytical and computational study of the (3 + 1)-dimensional Fornberg-Whitham (FW) equation, a highly nonlinear partial differential equation modeling complex wave interactions in multidimensional dispersive media. Employing Hirota’s bilinear method, we derive explicit lump and multi-soliton solutions, elucidating their dynamic interaction patterns and stability properties. To complement these findings, we develop a robust physics-informed neural network (PINN) framework to numerically solve the FW equation, capturing challenging rogue and breather wave phenomena with high accuracy. Comprehensive numerical experiments validate the PINN model against analytical benchmarks, demonstrating its capability to handle high-dimensional nonlinearities and mixed derivatives. These results provide critical insights into multidimensional wave dynamics and establish a hybrid approach that effectively blends classical soliton theory with modern machine learning, paving the way for future research in nonlinear wave propagation, fluid dynamics, and applied physics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101330"},"PeriodicalIF":0.0,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-11DOI: 10.1016/j.padiff.2025.101328
M. Nurul Islam , M. Al-Amin , M. Ali Akbar
In this study, we examine the conformal space-time fractional nonlinear Schrödinger (NLS) model and derive several new closed-form optical soliton solutions using an interoperable auxiliary-equation method. By applying a fractional wave transformation, the original model is converted into a nonlinear equation formulated in terms of conventional derivatives. The NLS model serves as an essential framework for characterizing wave propagation in nonlinear optical media, accounting for the factors that influence signal integrity and data transmission in optical fiber networks. For this model, we obtain new exact soliton solutions expressed through exponential, trigonometric, hyperbolic, and rational function forms. These optical soliton solutions are then employed to analyze how various model parameters affect their behavior, with numerical simulations carried out in Wolfram Mathematica. The numerical simulations of the derived solutions reveal periodic, kink-type, singular periodic, and other soliton-like behaviors. The findings indicate that the proposed method is both robust and efficient, making it a valuable tool for deriving optical soliton solutions in other fractional nonlinear models, especially those relevant to optical fiber communication systems.
{"title":"An investigation of novel closed form soliton solutions of the space-time fractional nonlinear Schrödinger model in optical fibers","authors":"M. Nurul Islam , M. Al-Amin , M. Ali Akbar","doi":"10.1016/j.padiff.2025.101328","DOIUrl":"10.1016/j.padiff.2025.101328","url":null,"abstract":"<div><div>In this study, we examine the conformal space-time fractional nonlinear Schrödinger (NLS) model and derive several new closed-form optical soliton solutions using an interoperable auxiliary-equation method. By applying a fractional wave transformation, the original model is converted into a nonlinear equation formulated in terms of conventional derivatives. The NLS model serves as an essential framework for characterizing wave propagation in nonlinear optical media, accounting for the factors that influence signal integrity and data transmission in optical fiber networks. For this model, we obtain new exact soliton solutions expressed through exponential, trigonometric, hyperbolic, and rational function forms. These optical soliton solutions are then employed to analyze how various model parameters affect their behavior, with numerical simulations carried out in Wolfram Mathematica. The numerical simulations of the derived solutions reveal periodic, kink-type, singular periodic, and other soliton-like behaviors. The findings indicate that the proposed method is both robust and efficient, making it a valuable tool for deriving optical soliton solutions in other fractional nonlinear models, especially those relevant to optical fiber communication systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101328"},"PeriodicalIF":0.0,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791938","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 : 2025-12-10DOI: 10.1016/j.padiff.2025.101331
M. Al-Amin , M.Nurul Islam , M.Ali Akbar
In this study, we suggest an improved modified simplest equation (IMSE) approach to obtain distinct analytical solutions of the three-dimensional nonlinear fractional Wazwaz-Benjamin-Bona-Mahony (FWBBM) model associated with the conformable derivative. The suggested IMSE approach extends the classical simplest equation approach by introducing four new solutions, enhancing its efficiency and generality for solving nonlinear fractional partial differential equations. This approach yields fifteen solitary wave solutions for each equation of the three-dimensional FWBBM model, including trigonometric, hyperbolic, algebraic, and mixed-function types. The obtained solutions describe diverse soliton shapes such as bell-shaped, anti-bell-shaped, singular, and periodic solitons, which illustrate the rich dynamical behavior of nonlinear dispersive waves. The physical implications of these solutions are analyzed through three-, two-dimensional, and contour plots depicted through Mathematica, showing that the fractional-order parameter significantly affects soliton amplitude, shape, and stability. Comparisons with existing analytical methods, including the tanh-coth and -expansion techniques, confirm the precedence and broader applicability of the IMSE method. This approach provides deeper insights into nonlinear wave propagation and soliton dynamics and provides a powerful analytical tool for multidimensional fractional models in plasma physics, fluid mechanics, and optical systems.
在这项研究中，我们提出了一种改进的修正最简单方程（IMSE）方法来获得三维非线性分数阶wazwazi - benjamin - bona - mahony （FWBBM）模型的不同解析解。本文提出的IMSE方法扩展了经典的最简单方程方法，引入了四个新的解，提高了求解非线性分数阶偏微分方程的效率和通用性。这种方法为三维FWBBM模型的每个方程提供了15个孤波解，包括三角、双曲、代数和混合函数类型。得到的解描述了钟形孤子、反钟形孤子、奇异孤子和周期孤子等不同形状的孤子，说明了非线性色散波丰富的动力学行为。通过Mathematica绘制的三维、二维和等高线图分析了这些解的物理含义，表明分数阶参数显著影响孤子振幅、形状和稳定性。与现有的分析方法，包括tanh-coth和exp（−ϕ（ω））-展开技术的比较，证实了IMSE方法的优先性和更广泛的适用性。这种方法为非线性波传播和孤子动力学提供了更深入的见解，并为等离子体物理、流体力学和光学系统中的多维分数模型提供了强大的分析工具。
{"title":"An improved modified simplest equation method for exact solitary wave solutions of the three-dimensional nonlinear fractional wazwaz-benjamin-bona-mahony model","authors":"M. Al-Amin , M.Nurul Islam , M.Ali Akbar","doi":"10.1016/j.padiff.2025.101331","DOIUrl":"10.1016/j.padiff.2025.101331","url":null,"abstract":"<div><div>In this study, we suggest an improved modified simplest equation (IMSE) approach to obtain distinct analytical solutions of the three-dimensional nonlinear fractional Wazwaz-Benjamin-Bona-Mahony (FWBBM) model associated with the conformable derivative. The suggested IMSE approach extends the classical simplest equation approach by introducing four new solutions, enhancing its efficiency and generality for solving nonlinear fractional partial differential equations. This approach yields fifteen solitary wave solutions for each equation of the three-dimensional FWBBM model, including trigonometric, hyperbolic, algebraic, and mixed-function types. The obtained solutions describe diverse soliton shapes such as bell-shaped, anti-bell-shaped, singular, and periodic solitons, which illustrate the rich dynamical behavior of nonlinear dispersive waves. The physical implications of these solutions are analyzed through three-, two-dimensional, and contour plots depicted through Mathematica, showing that the fractional-order parameter significantly affects soliton amplitude, shape, and stability. Comparisons with existing analytical methods, including the tanh-coth and <span><math><mrow><mtext>exp</mtext><mo>(</mo><mrow><mo>−</mo><mi>ϕ</mi><mo>(</mo><mi>ω</mi><mo>)</mo></mrow><mo>)</mo></mrow></math></span>-expansion techniques, confirm the precedence and broader applicability of the IMSE method. This approach provides deeper insights into nonlinear wave propagation and soliton dynamics and provides a powerful analytical tool for multidimensional fractional models in plasma physics, fluid mechanics, and optical systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101331"},"PeriodicalIF":0.0,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792018","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 : 2025-12-09DOI: 10.1016/j.padiff.2025.101326
Sharmin Sultana Shanta , M. Ali Akbar
The monkeypox virus has become a major global health concern due to its rapid spread. Medical intervention and isolation are essential to control the outbreak until an effective treatment is discovered. In this article, we develop a fractional SEIQR model to study the transmission dynamic of the monkeypox virus by including key epidemiological factors and memory effects. The nonlinear model describing the spread of viruses is investigated using the fractional Laplace-Adomian decomposition method (LADM), a powerful analytical technique to address complex infectious disease models. The results are strictly validated by comparing them with those derived from the fractional fourth-order Runge-Kutta (RK4) method. The results demonstrate strong agreement for , which confirms the reliability of the fractional framework. The error analysis shows that adding more LADM terms increases the accuracy. Positivity and sensitivity analyses confirm the model is biologically valid and show that early detection, isolation, quarantine, and reduced contact strongly affect infection levels. The phase portraits and contour plots provide insight into system behavior and threshold conditions. The study highlights the effectiveness of fractional LADM in describing nonlocal and memory-driven dynamics that cannot be represented in classical models.
{"title":"Fractional mathematical modeling on monkeypox using the Laplace-Adomian decomposition method","authors":"Sharmin Sultana Shanta , M. Ali Akbar","doi":"10.1016/j.padiff.2025.101326","DOIUrl":"10.1016/j.padiff.2025.101326","url":null,"abstract":"<div><div>The monkeypox virus has become a major global health concern due to its rapid spread. Medical intervention and isolation are essential to control the outbreak until an effective treatment is discovered. In this article, we develop a fractional SEIQR model to study the transmission dynamic of the monkeypox virus by including key epidemiological factors and memory effects. The nonlinear model describing the spread of viruses is investigated using the fractional Laplace-Adomian decomposition method (LADM), a powerful analytical technique to address complex infectious disease models. The results are strictly validated by comparing them with those derived from the fractional fourth-order Runge-Kutta (RK4) method. The results demonstrate strong agreement for <span><math><mrow><mi>ζ</mi><mo>=</mo><mn>0.99</mn></mrow></math></span>, which confirms the reliability of the fractional framework. The error analysis shows that adding more LADM terms increases the accuracy. Positivity and sensitivity analyses confirm the model is biologically valid and show that early detection, isolation, quarantine, and reduced contact strongly affect infection levels. The phase portraits and contour plots provide insight into system behavior and threshold conditions. The study highlights the effectiveness of fractional LADM in describing nonlocal and memory-driven dynamics that cannot be represented in classical models.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101326"},"PeriodicalIF":0.0,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145760655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study presents a mathematical model to explore two-dimensional, time-dependent fluid flow towards a stagnation point over a Riga plate, under the influence of magnetohydrodynamics (MHD), activation energy, and a higher-order chemical reaction. The surface of the Riga plate is lined with magnets and electrodes, arranged in a structured manner. The research investigates the effects of radiation and Joule heating on fluid motion and includes an entropy generation analysis based on the second law of thermodynamics. The partial differential equations (PDEs) that govern the physical system are reduced to ordinary differential equations (ODEs) via similarity variables, and solved using both the shooting method and the bvp4c algorithm. Results indicate that the unsteadiness parameter increases skin friction by 5.53 %, while the heat source parameter reduces heat transfer by up to 33.4 %. Entropy generation is found to rise with increasing Brinkman number and concentration difference, whereas higher temperature differences lower entropy production. The combined effects of Lorentz force, exponential chemical reaction, internal heat generation, and suction/injection within an unsteady Riga plate configuration have not been explored previously. Furthermore, the inclusion of irreversibility analysis enhances the novelty and provides deeper insight into energy dissipation mechanisms and system efficiency, offering valuable guidance for designing advanced MHD-based thermal control and energy systems. These numerical results are well aligned with existing literature, reinforcing the reliability of the analysis and highlighting its significance for energy-efficient thermal system design.
{"title":"Entropy generation and MHD flow characteristics of unsteady Williamson fluid toward a stagnation point over a vertical Riga plate","authors":"Hassan Shahzad , Dur-E-Shehwar Sagheer , Hajra Batool , Maryam Ali Alghafli , Nabil Mlaiki","doi":"10.1016/j.padiff.2025.101321","DOIUrl":"10.1016/j.padiff.2025.101321","url":null,"abstract":"<div><div>This study presents a mathematical model to explore two-dimensional, time-dependent fluid flow towards a stagnation point over a Riga plate, under the influence of magnetohydrodynamics (MHD), activation energy, and a higher-order chemical reaction. The surface of the Riga plate is lined with magnets and electrodes, arranged in a structured manner. The research investigates the effects of radiation and Joule heating on fluid motion and includes an entropy generation analysis based on the second law of thermodynamics. The partial differential equations (PDEs) that govern the physical system are reduced to ordinary differential equations (ODEs) via similarity variables, and solved using both the shooting method and the bvp4c algorithm. Results indicate that the unsteadiness parameter increases skin friction by 5.53 %, while the heat source parameter reduces heat transfer by up to 33.4 %. Entropy generation is found to rise with increasing Brinkman number and concentration difference, whereas higher temperature differences lower entropy production. The combined effects of Lorentz force, exponential chemical reaction, internal heat generation, and suction/injection within an unsteady Riga plate configuration have not been explored previously. Furthermore, the inclusion of irreversibility analysis enhances the novelty and provides deeper insight into energy dissipation mechanisms and system efficiency, offering valuable guidance for designing advanced MHD-based thermal control and energy systems. These numerical results are well aligned with existing literature, reinforcing the reliability of the analysis and highlighting its significance for energy-efficient thermal system design.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101321"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145623825","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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