Partial Differential Equations in Applied Mathematics最新文献

{"title":"Thermal radiation effect on fractional MHD Couette Flow of Jeffrey fluid in a vertical channel with activation energy and Joule Heating","authors":"Paul M. Matao ,&nbsp;Jumanne Mng’ang’a ,&nbsp;B. Prabhakar Reddy","doi":"10.1016/j.padiff.2025.101251","DOIUrl":"10.1016/j.padiff.2025.101251","url":null,"abstract":"<div><div>This study investigates the consequence of thermal radiation on the fractional magnetohydrodynamic (MHD) Couette flow of a Jeffrey fluid in a vertical channel, incorporating the influences of activation energy and Joule heating. The mathematical model is derived using appropriate governing equations that account for the non-Newtonian behavior of the Jeffrey fluid, combined with the impacts of thermal radiation, magnetic field, and activation energy mechanisms. The classical mathematical framework has been transformed into a system of fractal fractional-order derivatives using the Caputo–Fabrizio derivative operator. To solve these systems, the finite difference technique was employed. The behavior of fluid flow fields in response to several significant parameters was analyzed and represented graphically. It is ascertained that velocity distribution upsurges as Hall current parameter rises, while a more substantial effect from the Jeffrey fluid parameter results in a decrease in the velocity field. Additionally, thermal field profiles exhibited higher values in response to increased thermal radiation and Joule heating parameters, whereas the temperature distribution showed a decline with improving in Hall current parameter values. The concentration field improved with higher activation energy parameter values, in contrast to the opposite trend observed with temperature difference and chemical reaction parameters. Furthermore, it is remarked that fractal fractional-order derivatives operator produced a more pronounced boundary layer compared to both fractional and classical models. It is ascertained that the Nusselt number showing a 15.7% improvement in thermal efficiency as thermal radiation varied from 2 to 4. These findings are important for applications in geothermal energy extraction, and biomedical engineering.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101251"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144557626","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":"Detailed analysis under fully constrained and relaxed boundary conditions of linear fields in the vicinity of a corner","authors":"Ayelet Goldstein,&nbsp;Ofer Eyal,&nbsp;Jorge Berger","doi":"10.1016/j.padiff.2025.101244","DOIUrl":"10.1016/j.padiff.2025.101244","url":null,"abstract":"<div><div>This work examines the behavior of fields near corners under various boundary conditions (BCs), focusing on singularities arising from fully constrained and relaxed BCs. We analyze this behavior across diverse physical systems governed by similar equations, including electromagnetism, superconductivity, and two-phase fluid flow. The corner geometry presents a challenge due to potentially diverging field solutions as the corner is approached (r<span><math><mo>→</mo></math></span> 0). This motivates the investigation of relaxed BCs, which regularize the field by introducing a characteristic length (Ls) that relates the field’s value to its normal derivative at the boundary.</div><div>We explore both single-medium (single-phase) and double-medium (two-phase) systems. While prior research has addressed relaxed BCs in specific contexts, their application to corners, particularly in diverse physical systems, remains under-explored. We develop a series solution method to analyze the field behavior near the corner under different BCs. Concrete examples illustrate the theoretical framework, examining both fully constrained and relaxed scenarios. The implications of this work extend to fields such as fluid mechanics, electromagnetism, and heat transfer.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101244"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144557625","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":"Analytical simulation of the nonlinear Caputo fractional equations","authors":"Ali Ahadi ,&nbsp;Seyed Mostafa Mousavi ,&nbsp;Amir Mohammad Alinia ,&nbsp;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":"2025-09-01","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}

{"title":"Geometric properties of Smarandache ruled surfaces generated by integral binormal curves in Euclidean 3-space","authors":"Ayman Elsharkawy ,&nbsp;Hanene Hamdani ,&nbsp;Clemente Cesarano ,&nbsp;Noha Elsharkawy","doi":"10.1016/j.padiff.2025.101298","DOIUrl":"10.1016/j.padiff.2025.101298","url":null,"abstract":"<div><div>This paper investigates the geometric properties of Smarandache ruled surfaces generated by integral binormal curves in the Euclidean 3-space <span><math><msup><mrow><mi>E</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. Specifically, we study four types of Smarandache ruled surfaces: the <span><math><mrow><mi>t</mi><mi>n</mi></mrow></math></span>, <span><math><mrow><mi>t</mi><mi>b</mi></mrow></math></span>, <span><math><mrow><mi>n</mi><mi>b</mi></mrow></math></span>, and <span><math><mrow><mi>t</mi><mi>n</mi><mi>b</mi></mrow></math></span> surfaces, each defined by different combinations of the tangent, normal, and binormal vectors of the integral curves. For each type of surface, we derive the parametric representations and compute the fundamental geometric properties, including the striction lines, distribution parameters, and the first and second fundamental forms. Additionally, we provide explicit expressions for the Gaussian and mean curvatures, which characterize the local shape of the surfaces. We also analyze the geodesic curvature, normal curvature, and geodesic torsion associated with the base curves on these surfaces. Furthermore, we establish necessary and sufficient conditions for these surfaces to be developable or minimal. The paper concludes with detailed conditions under which the base curves can be classified as geodesic or asymptotic lines on the surfaces. The results are supported by rigorous proofs and illustrative examples, offering a comprehensive understanding of the geometric behavior of these Smarandache ruled surfaces.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101298"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931558","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":"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}