Partial Differential Equations in Applied Mathematics最新文献

{"title":"Results on multivalent Bessel functions associated with a new integral operator","authors":"Esther O. Davids ,&nbsp;Olubunmi A. Fadipe-Joseph ,&nbsp;Matthew O. Oluwayemi","doi":"10.1016/j.padiff.2025.101228","DOIUrl":"10.1016/j.padiff.2025.101228","url":null,"abstract":"<div><div>Many authors have considered several special functions and their applications in geometric function theory using different operators. Not much was known in literature on analytic functions associated with Bessel function using integral operator. Therefore, in this work, their geometric properties were obtained. Specifically, coefficient bounds, coefficients inequalities, growth and distortion theorems with other coefficient results for functions in these classes were established.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101228"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solution of Helmholtz eigenvalue problems with non-regular domains using the direct interpolation technique","authors":"Carlos Friedrich Loeffler ,&nbsp;Luciano de Oliveira Castro Lara ,&nbsp;Hercules de Melo Barcelos ,&nbsp;João Paulo Barbosa","doi":"10.1016/j.padiff.2025.101235","DOIUrl":"10.1016/j.padiff.2025.101235","url":null,"abstract":"<div><div>This work aims to evaluate the performance of the Direct Interpolation Boundary Element Method solving Helmholtz problems that present no regular geometric shapes. Using the radial basis functions, the Direct Interpolation Method approximates the non-self-adjoint kernel of the domain integral equations, which appear in many partial differential equations of mathematics, physics, and engineering. Modeling the Helmholtz Equation, the Direct Interpolation Method approximates the inertia term by a sequence of radial basis functions. The technique has been used successfully in Poisson, Diffusive-advective, and Helmholtz problems, considering regular geometries and taking analytical solutions as a reference for performance evaluation. This paper evaluates the effects of the slenderness of the domain and the introduction of cuts on the boundary regarding the accuracy. Reference solutions are generated through Finite Element Method simulations using fine meshes.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101235"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-Classical Modeling of Cosserat Fluid-Structure Interaction System for Analyzing Micro-Rotational Effects of Micro-Viscosities on Flow Velocity Fields","authors":"Nazim Hussain Hajano ,&nbsp;Muhammad Sabeel Khan ,&nbsp;Mumtaz Ali Kaloi ,&nbsp;M. Asif Memon ,&nbsp;Lisheng Liu","doi":"10.1016/j.padiff.2025.101227","DOIUrl":"10.1016/j.padiff.2025.101227","url":null,"abstract":"<div><div>Conservation laws of classical continuum mechanics are naturally written in the Eulerian frame where only the expression of the stress tensor distinguish fluids and solid structures, usually with Newtonian’s hypothesis for fluids and Helmholtz potential of energy for hyper-elastic solid structures. In the recent literature, the benchmark solutions of fluid-structure interaction (FSI) phenomenon present in a classical continuum mechanics have been used to study different flow characteristics by taking into account a non-classical Cosserat fluid-structure interaction (CFSI) problems. In these studies, different micro-structural characteristics of flow velocity fields have been analyzed by validating results in a non-classical framework. However, the micro-rotational effects of micro-viscosity parameters λ which combines shear spin viscosity β and rotational spin viscosityγare very significant in analyzing the behavior of flow fields in such coupling problems still needs to be improved and extended at the micro- structural level. Therefore, this paper extends the scope of the study for analyzing micro-rotational effects of micro-viscosity parameters of the Cosserat fluid on flow velocity fields by employing the monolithic Eulerian approach to such non-classical coupling problem. The conservation laws of continuum mechanics are used to derive the governing dynamics and variational formulation of the present Cosserat fluid-structures system. The problem domains are discretized using the proposed schemes and algorithm for computer simulations is implemented with publicly available software <em>freefem</em>++. Results of the present study indicates that, the micro-viscosity parameter λ effects the micro-rotation velocity field <strong>ω</strong> significantly as compare to the velocity field <strong>u</strong> such that fluid particles undergo large micro-rotation near the control point <em>A</em> in the computational domain. Further, the micro-rotational effects of fluid particles are found minimum on the axis of symmetry of the control point <em>A</em> and vanishes on the computational boundaries. Finally, the color visualizations of the micro-rotational velocity profile with contour plots are also presented and the study is concluded with some future recommendations and limitations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101227"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144230099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermodynamic analysis on the SWCNT-EG-based nanofluid flow in a squeezing horizontal channel under the influence of thermal radiation and viscous dissipation","authors":"Sampath Kumar V.S. ,&nbsp;Ali J. Chamkha ,&nbsp;Devaki B. ,&nbsp;Nityanand P. Pai ,&nbsp;Pareekshith G. Bhat ,&nbsp;Rollin Preetha Vaz ,&nbsp;Vasanth K.R. ,&nbsp;Ganesh Kumar K. ,&nbsp;Ashwin Kumar Devaraj","doi":"10.1016/j.padiff.2025.101234","DOIUrl":"10.1016/j.padiff.2025.101234","url":null,"abstract":"<div><div>The current study theoretically examines the behaviour of heat transfer in the ethylene glycol (EG)-based nanofluid containing single-walled carbon nanotubes (SWCNT) flow that is squeezed between a pair of horizontal parallel plates. Due to its superior thermal conductivity, EG-based SWCNT nanofluids are well-suited for use in high-performance cooling systems, including automotive radiators, electronic thermal management, industrial refrigeration, and heat exchangers across power generation, HVAC, and chemical processing applications. This study further focuses on analysing the thermal radiation effect on the thermodynamic properties of the viscous dissipated nanofluid flow. Employing suitable similarity transformations, the equations that govern flow and energy arising in the study are converted into a set of non-linear ordinary differential equations (ODEs), after which an approximate analytic solution is achieved using the homotopy perturbation method (HPM). This study mainly emphasizes on investigating the influence of distinct pertinent physical parameters on the velocity distribution curves, skin friction coefficient, temperature fields, and heat transfer rate. The HPM results are further compared with those of the classical finite difference method (FDM). It is evident from the current study that an elevation in the squeezing parameter and the Eckert number enhances the Nusselt number and temporal distribution curve. However, an elevation in the radiation parameter decreases the Nusselt number.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101234"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dark lump collision phenomena to a nonlinear evolution model in harmonic crystals","authors":"Muhammad Abubakar Isah ,&nbsp;Asif Yokus ,&nbsp;Ibrahim Isah","doi":"10.1016/j.padiff.2025.101214","DOIUrl":"10.1016/j.padiff.2025.101214","url":null,"abstract":"<div><div>In this paper, we examine the innovative KdV model, which has a profound impact on our understanding of a range of nonlinear occurrences of ion-acoustic waves in plasma and acoustic waves in harmonic crystals. Using the appropriate transformations, Hirota bilinearization is performed to generate the solutions. Using trigonometric, hyperbolic, and exponential functions, we generate collision aspects between lumps and other solutions in order to establish some more interaction solutions with some innovative physical characteristics. We obtain the two-wave, dark lump wave and lump-periodic solutions. The identified solutions are visually represented. In the fields of shallow-water waves, ion-acoustic waves in plasma, and acoustic waves in harmonic crystals, the current work is extensively exploited to describe a variety of remarkable physical events. To ensure the accuracy of the result, all the obtained solutions are placed in the model.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101214"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144262117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exploring the dynamics of multiplicative noise on the fractional stochastic Fokas-Lenells equation","authors":"Ali R. Ansari ,&nbsp;Adil Jhangeer ,&nbsp;Beenish ,&nbsp;Mudassar Imran ,&nbsp;Abdallah M. Talafha","doi":"10.1016/j.padiff.2025.101232","DOIUrl":"10.1016/j.padiff.2025.101232","url":null,"abstract":"<div><div>In this study, the fractional-stochastic Fokas-Lenells equation is considered in the Stratonovich framework. The new extended direct algebraic method is applied to construct various types of fractional solutions, including trigonometric, complex, hyperbolic, and exponential forms. Given the equation’s broad applications in telecommunication systems, complex system theory, quantum field theory, and quantum mechanics, the derived solutions have potential to model a variety of significant physical phenomena. To further illustrate the influence of multiplicative noise and fractional derivatives, multiple 3D plots are presented, highlighting their impact on the analytical behavior of the system. Secondly , by applying a Galilean transformation, the model is reformulated into a planar dynamical system, allowing for in-depth qualitative analysis. The sensitivity analysis of the model is performed, along with an examination of quasi-periodic patterns emerging from perturbations. The simulation results reveal that adjusting the amplitude and frequency parameters significantly alters the dynamic behavior of the system. The quasi-periodic behavior is further analyzed through time analysis, multi-stability, and Lyapunov exponents. Our results highlight the impact of the method on system dynamics and demonstrate its effectiveness in studying solitons and phase behavior in nonlinear models. These findings offer new insights into how the proposed approach can induce significant changes in system dynamics, emphasizing its utility in the analysis of soliton solutions and phase visualizations in various nonlinear models. By generating state-dependent oscillations, multiplicative noise has a substantial impact on the dynamics of the system. These fluctuations can either improve or decrease stability and result in complicated behaviors. The completion of stochastic systems affected by internal or external noise sources requires an understanding of this interaction.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101232"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144240984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computational analysis and wave propagation behavior of hyper-geometric soliton waves in plasma physics via the auxiliary equation method","authors":"M. Al-Amin ,&nbsp;M. Nurul Islam ,&nbsp;M. Ali Akbar","doi":"10.1016/j.padiff.2025.101231","DOIUrl":"10.1016/j.padiff.2025.101231","url":null,"abstract":"<div><div>This study investigate the widely used nonlinear fractional Kairat-II (K-II) model, which is used to explain the differential geometry of curves and equivalence aspects. Numerous vital incidents can be analyzed via the Kairat-II (K-II) model, likely the optical pulse propagation behaviors inside optical fibers and plasma. The Kairat-II (K-II) model is a vital mathematical model in the domain of science and engineering applications. This article computationally and analytically investigates the nonlinear fractional Kairat-II (K-II) model by using the auxiliary equation (AE) method through the renowned truncated M-fractional derivative. We have established several newer, practical, efficient and comprehensive closed form traveling wave solutions of the model. Moreover, we examine the influence of fractional parameters on signal transmission through optical fibers and other related wave propagations by generating 3D graphs of the established solutions. The established results confirm the effectiveness, efficiency and reliability of the considered method.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101231"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fractional-order model for two-strain Monkeypox virus: Analytical and numerical insights with optimal control strategies","authors":"Amr Elsonbaty ,&nbsp;A. El-Mesady","doi":"10.1016/j.padiff.2025.101229","DOIUrl":"10.1016/j.padiff.2025.101229","url":null,"abstract":"<div><div>In this study, we explore the dynamics of a proposed fractional-order model for human-to-human infections with dual strain Monkeypox viruses (MPVs). In addition, a suggested optimal control measures are investigated to manage the disease outbreaks within the community, which helps achieving good health and well-being goal of Sustainable Development Goals (SDGs). First, a comprehensive analytical study of the model is introduced to examine its essential properties, including existence, uniqueness, non-negativity, and boundedness of solutions. The equilibrium points of the model are found and a thorough stability analysis is conducted for each steady state. The possible bifurcation scenarios, that can be exhibited by the model, are also explored. The basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is computed and the impacts of key parameters are examined through detailed sensitivity analysis. Then, the time-dependent control variables are employed to formulate a fractional optimal control problem (FOCP) for the present model, where Pontryagin’s maximum principle (PMP) is used to constitute the necessary optimality conditions (NOCs). Numerical experiments are carried out to validate theoretical findings and assess the biological implications of the applied control measures. The numerical results indicate that the proposed combination of control strategies can effectively minimize the infection control costs while effectively working towards eradicating the infection.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101229"},"PeriodicalIF":0.0,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Developing and applying cubic spline method for the solution of boundary value problems in complex physical and engineering systems","authors":"Aasma Khalid ,&nbsp;Inamul Haq ,&nbsp;Akmal Rehan ,&nbsp;M.S. Osman","doi":"10.1016/j.padiff.2025.101224","DOIUrl":"10.1016/j.padiff.2025.101224","url":null,"abstract":"<div><div>It has long been a concern of researchers to address the challenges of solving higher-order differential equations. In order to approximate 11th-order boundary value problems (BVPs), this work presents a novel numerical approach that combines decomposition techniques with polynomial and Non-Polynomial Splines of third order. The method starts with a decomposition process that breaks down 11th-order BVPs into a system of second-order BVPs, breaking the problem down into smaller, more manageable parts. First-order derivatives are approximated using finite central differences, and each second-order ordinary differential equation is solved using both spline methods. These methods improve accuracy and efficiency when handling complex BVPs by providing a thorough framework for solving high-order differential equations. Comparing numerical responses with the precise response on a variety of examples was part of the numerical evaluations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101224"},"PeriodicalIF":0.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two-phase micropolar nanofluid flow in an isothermal extending porous sheet with heat radiation and chemical interaction: Numerical study","authors":"MD. Shamshuddin ,&nbsp;Fakhraldeen Gamar ,&nbsp;S.O. Salawu ,&nbsp;B. Prabhakar Reddy","doi":"10.1016/j.padiff.2025.101226","DOIUrl":"10.1016/j.padiff.2025.101226","url":null,"abstract":"<div><div>This study examines the capabilities of thermal radiation and chemical reactions on the transport of a micropolar nanofluid flow along a vertical sheet contiguous with an isothermal porous structure. Using similarity variable techniques, the partial differential equations (PDEs) which elucidate the envisioned model yield nonlinear ordinary differential equations (ODEs) in their self-similar form. The fourth-order Runge-Kutta method in combination with the shooting techniques is used to solve them. The important characteristics of the fluid speed, thermal transport, and solute profiles are explained by the graphs and friction-drag, rate of thermal and solutal portages by the tables. This analysis shows that increasing Brownian motion and thermophoresis outcomes improve the concentration profile, whereas augmenting chemical reaction rate specifications and Lewis number has shown a reverse effect. The fluid speed increased by the micropolar parameter, but the angular velocity faced opposite erudition. The modified Forchheimer and Darcy factor was initiated to improve fluid velocity. The temperature field was enlarged by radiation, Darcy term, and heat source, but it was decreased by the micropolar parameter. Further, the findings, which include a table comparing local boundary friction, heat, and mass transfer rates at different parameter values, are consistent with previous studies. These results provide predictive insights into flow patterns, temperature distribution, and fluid concentration, all of which have significant consequences for engineering efficiency.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101226"},"PeriodicalIF":0.0,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144124480","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}