Partial Differential Equations in Applied Mathematics最新文献

{"title":"Thermal and flow characteristics of hybrid nanofluids in free-forced convection under suction/blowing effects","authors":"Sharanayya Swami ,&nbsp;Ali B M Ali ,&nbsp;Suresh Biradar ,&nbsp;Jagadish V Tawade ,&nbsp;M. Ijaz Khan ,&nbsp;Nitiraj Kulkarni ,&nbsp;Dilsora Abduvalieva ,&nbsp;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":"2025-09-01","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}

{"title":"Campatibility of solitons within the frame work of Estevez-Mansfield-Clarkson equation","authors":"Nauman Ahmed ,&nbsp;Sidra Ghazanfar ,&nbsp;Zunaira ,&nbsp;Muhammad Z. Baber ,&nbsp;Ilyas Khan ,&nbsp;Osama Oqilat ,&nbsp;Wei Sin Kohh","doi":"10.1016/j.padiff.2025.101286","DOIUrl":"10.1016/j.padiff.2025.101286","url":null,"abstract":"<div><div>This work suggests single-wave solutions for the Estevez-Mansfield-Clarkson (EMC) and linked sine-Gordon equations. The shape generation process in droplet form is studied using these model equations. For accurate wave and solitary wave solutions, in addition to many mathematical and physical research methods. There is nonlinear dispersion according to the EMC equation. It is feasible to generalize the Estevez-Mansfield integrable. Precise wave solutions, including kink, solitary, rational, single, and anti-kink, may be obtained by modifying the generalized exponential rational function technique. These changes may be advantageous in several scientific and technological domains. A novel approach to the precise solution of nonlinear partial differential equations is presented in this paper. The strategy’s main objective is to increase the applicability of the exponential rational function technique.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101286"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018459","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 assessment of local thermal non-equilibrium effects on non-darcy chemical reactive flow of boger hybrid nanofluid with elastic deformation","authors":"Mostafa Mohamed Okasha ,&nbsp;Mohammed Qader Gubari ,&nbsp;Hawzhen Fateh M. Ameen ,&nbsp;Munawar Abbas ,&nbsp;Muyassar Norberdiyeva ,&nbsp;Wei Sin Koh ,&nbsp;Ilyas Khan","doi":"10.1016/j.padiff.2025.101260","DOIUrl":"10.1016/j.padiff.2025.101260","url":null,"abstract":"<div><div>This study examines the effects of velocity slip and local thermal non-equilibrium on the non-Darcy chemical convective flow of a Boger hybrid nanofluid across a sheet. The energy equation-based on local thermal non-equilibrium model provides outstanding heat transmission for solid and liquid phases. The two thermal distributions for the liquid and solid phases are basically used in this method. The hybrid nanoliquid (<em>SiC</em> − <em>C</em>o₃O₄/<em>DO</em>) flow model consist of nanoparticles of silicon carbide (<em>SiC</em>) and Cobalt oxide (Co₃O₄) dissolved in diathermic oil. This model can be used in sectors of the economy where improved heat transfer is essential, like electronic cooling systems, automotive thermal systems, and energy-efficient heat exchangers. The concept is also applicable to the design of materials for use in aerospace applications, where it is necessary to precisely regulate the mechanical and thermal properties under conditions of high stress and temperature gradients. The Bvp4c method is used to numerically solve the model equation system once all relevant similarity variables have been decreased. Outcomes display that Boger hybrid nanofluid shows increase flow and decline the thermal and concentration distributions as increasing the solvent percent and Stefan blowing parameters values.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101260"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144757968","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":"A study on fractional-order mathematical analysis for inspecting the spread of the leukemia virus","authors":"Rezaul Karim ,&nbsp;M. A. Bkar Pk ,&nbsp;M. Ali Akbar ,&nbsp;Pinakee Dey","doi":"10.1016/j.padiff.2025.101297","DOIUrl":"10.1016/j.padiff.2025.101297","url":null,"abstract":"<div><div>Leukemia is the name for a blood cancer that develops in the bone marrow. Leukemia is a global public health issue caused by the uncontrolled growth of immature white blood cells in the bloodstream. In this study, we consider a fractional-order five-compartment mathematical model (MM) of leukemia, which includes susceptible blood cells<span><math><mrow><mspace></mspace><msub><mi>S</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, infected blood cells <span><math><mrow><msub><mi>I</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, cancer cells <span><math><mrow><msub><mi>C</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, immune blood cells <span><math><mrow><msub><mi>W</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, cytokine cells <span><math><mrow><msub><mi>C</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, and we analyze the dynamics of transmission of the disease. We developed a model to examine the spread of the leukemia virus and analyze the effects of adoptive T-cell therapy. This study presents a model of the well-known leukemia virus utilizing Caputo fractional order (CFO) and Beta derivatives. In this, the extended system characterizing the virus spread is addressed using two analytical methods: the Laplace perturbation method (LPM) and the Homotopy decomposition method (HDM). Iterative schemes were employed to obtain specific solutions of the extended system, and numerical simulations were conducted based on selected theoretical parameters. Moreover, the concerned analytical solutions that have been found using the methods are compared. The corresponding plots against various orders of the differentiations are plotted using specific values for the model’s parameters. We emphasize the significance of fractional-order (FO) modeling in understanding the spread of leukemia and highlight the critical need for global access to this immunotherapy.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101297"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914036","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":"Formable transform Adomian decomposition method for solving nonlinear time-fractional diffusion equation","authors":"Alemu Senbeta Bekela ,&nbsp;Mesfin Mekuria Woldaregay","doi":"10.1016/j.padiff.2025.101271","DOIUrl":"10.1016/j.padiff.2025.101271","url":null,"abstract":"<div><div>Nonlinear time-fractional diffusion equations (NTFDEs) are widely applied for modeling various natural processes like volcanic eruption, diffusion processes, earthquakes, brain tumors, and the dynamics of soil in water. Solving these problems is quite challenging. So, designing effective numerical approaches is an active research area. The fractional derivative used is the Caputo type. In this paper, we develop the hybrid series based method by combining the Formable transform and Adomian decomposition method (ADM) for treating the NTFDEs. The stability and convergence of the developed series based method have been investigated. The effectiveness of the introduced method is investigated by solving two test examples. The obtained numerical results show that the proposed method is efficient for solving NTFDEs and gives accurate results.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101271"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamical analysis and numerous signal transmission behavior of the nonlinear Pochhammer-Chree (PC) model via two consistent schemes","authors":"M. Al-Amin ,&nbsp;M․Nurul Islam ,&nbsp;M․Ali Akbar","doi":"10.1016/j.padiff.2025.101248","DOIUrl":"10.1016/j.padiff.2025.101248","url":null,"abstract":"<div><div>This investigation conducts a comprehensive analytical analysis of the renowned nonlinear Pochhammer-Chree (PC) model by utilizing two efficient methods. The nonlinear PC model stands as a robust tool for the analysis of movement of traveling waves in a substantially long cylindrical rod with a circular cross-section, and longitudinal wave such as sound and particle wave propagation through elastic medium. The PC model also plays very important role in explaining various natural and engineering applications. To establish these results, we employ the generalized exponential rational function (GERF) method and the auxiliary equation (AE) method. The obtain results uncover numerous secrete dynamical characteristics of the model. Here, we also examine the influences of wave propagation velocity parameter on the attained solutions to understand the inner mechanism and dynamical signal transmission behavior of the related phenomenon. The gestures of obtained results are explained by representing the 3-dimensional (3D) and 2-dimensional (2D) shapes. The attained solutions demonstrate that the employed techniques are straightforward, reliable, functional and more effective to extracting soliton solutions of numerous nonlinear models.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101248"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144472220","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":"An iterative method for solving sparse linear algebraic systems with continuum solution dependent right-hand side for elliptic partial differential equations","authors":"Sudipta Lal Basu ,&nbsp;Kirk M. Soodhalter ,&nbsp;Breiffni Fitzgerald ,&nbsp;Biswajit Basu","doi":"10.1016/j.padiff.2025.101236","DOIUrl":"10.1016/j.padiff.2025.101236","url":null,"abstract":"<div><div>Krylov subspace iterative methods such as bi-conjugate gradients stabilized (BiCGStab) to approximately solve sparse linear algebraic systems are well known. However, there are certain instances in real-world engineering applications with underlying governing partial differential equation where the discretized right-hand side can only be exactly determined using the unavailable continuum solution. In such cases, an iterative method such as BiCGStab may not converge to a physically correct solution or may diverge completely. Such a method must be modified to accommodate inexact knowledge of the discrete right-hand side, using an updating scheme as the iteration proceeds. In this paper, we present such an updating strategy for physical problems governed by elliptic partial differential equations. This strategy must be performed in a numerically stable manner, which we also discuss. We present this as a modified BiCGStab iteration and investigate its effectiveness on both test problems, wherein it is shown to perform well and agrees with the analytical solutions, and on some more realistic problems arising in the study of Hele-Shaw flow, composite materials and power generation from wind farms.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101236"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513917","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":"Pricing basket options using Monte Carlo simulation employing Cholesky decomposition and variance reduction techniques under the 2D stochastic Black–Scholes equation","authors":"Youness Saoudi ,&nbsp;Khalid Jeaab ,&nbsp;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&amp;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":"2025-09-01","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}

{"title":"The Modified Homogeneous Balance Method for solving fractional Cahn–Allen and equal width equations","authors":"Francis Tuffour,&nbsp;Benedict Barnes,&nbsp;Isaac Kwame Dontwi,&nbsp;Kwaku Forkuoh Darkwah","doi":"10.1016/j.padiff.2025.101246","DOIUrl":"10.1016/j.padiff.2025.101246","url":null,"abstract":"<div><div>This paper presents exact solutions to the Fractional Cahn–Allen (FC–A) and the Fractional Equal Width (FEW) equations using the Modified Homogeneous Balance Method (MHBM). The MHBM transforms the FC–A and FEW equations into fractional ordinary differential equations via a wave transformation. By balancing the highest-order derivative with the leading nonlinear term, the method determines the appropriate polynomial degree. A fractional Riccati equation with a quadratic nonlinearity facilitates the construction of exact solutions without resorting to infinite series expansions. Compared to existing methods, the MHBM offers a finite and well-defined solution structure, avoiding the rigidity of the <span><math><mrow><mo>tan</mo><mfenced><mrow><mfrac><mrow><mi>ξ</mi><mrow><mo>(</mo><mi>η</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mfenced></mrow></math></span>-expansion method and the complexities associated with the Riemann–Hilbert and algebro–geometric methods. It also provides clearer criteria for convergence analysis than the <span><math><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>6</mn></mrow></msup></math></span>-expansion method. The MHBM accommodates various solution types, including trigonometric, hyperbolic, rational, and elliptic functions, with fewer parameter restrictions and potential for multi-wave structures. Numerical simulations shows that as the spatial variable <span><math><mi>x</mi></math></span> increases, the solitons tend to stabilize, and the plots for different values of the fractional order <span><math><mi>α</mi></math></span> closely aligned, indicating minor sensitivity to <span><math><mi>α</mi></math></span>. Furthermore, the FEW soliton exhibits a dense tiling structure along the time axis in its surface plot, while the FC–A soliton demonstrates a smooth kink-like transition along <span><math><mi>ξ</mi></math></span>, characteristic of solutions connecting two stable equilibrium states. These findings underscore the robustness and versatility of the MHBM in analyzing fractional nonlinear evolution equations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101246"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144562991","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 modeling of prophylactic measures on the transmission dynamics of measles: An optimal control analysis","authors":"Adedapo Chris Loyinmi ,&nbsp;Alani Lateef Ijaola","doi":"10.1016/j.padiff.2025.101259","DOIUrl":"10.1016/j.padiff.2025.101259","url":null,"abstract":"<div><div>In this study, we presented a fractional order transmission model to investigate the dynamics and potential controls for measles, in order to accurately represent the dynamics of its transmission. We propose a modified S, V, E, I and R (Susceptible, Vaccinated, Exposed, Infectious and Recovered individuals), a workable human population model with an incident rate equipped with a saturation factor to investigate the combined impact of three prophylactic techniques, which are public awareness, second dose vaccination and proper treatment in case of severity.. Here, we assumed there is a vaccinated population that has taken first dose in the proposed model. We established among other things, the parameter responsible for invasion, the reproductive number,<em>R</em>₀ is less than unity through the stability analysis and the numerical solution of the fractional order model was done using the Adams Bashforth predictor-corrector method. In addition, the effects of the prophylactic measures and the fractional order (α) were simulated and findings from the graphical solutions depict that these measures aid in flattening out the trajectory of the disease if measure are properly implemented.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101259"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680601","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}