Partial Differential Equations in Applied Mathematics最新文献

{"title":"Corrigendum to “Modulation instability, and dynamical behavior of solitary wave solution of time M- fractional Clannish Random Walker's Parabolic equation via two analytic techniques” [Partial Differential Equations in Applied Mathematics Volume 12, December 2024, 101011]","authors":"Mohammed Kbiri Alaoui , Mahtab Uddin , Md. Mamunur Roshid , Harun Or Roshid , M.S. Osman","doi":"10.1016/j.padiff.2024.101072","DOIUrl":"10.1016/j.padiff.2024.101072","url":null,"abstract":"","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101072"},"PeriodicalIF":0.0,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of Koo-Kleinstreuer-Li model water-based nanofluid: Interval Type 2 fuzzy approach","authors":"M.M. Nayak,&nbsp;S.R. Mishra,&nbsp;Rupa Baithalu","doi":"10.1016/j.padiff.2025.101086","DOIUrl":"10.1016/j.padiff.2025.101086","url":null,"abstract":"<div><div>The current study investigates the role of conducting nanofluid past a thin layer that is positioned horizontally while addressing uncertainties in the system using interval type-2 trapezoidal fuzzy sets [IT2TrFS]. The flow phenomena enrich due to the consideration of Brownian conductivity based on the Koo–Kleinstreuer–Li (KKL) model thermal conductivity. The modeled problem for the nanofluid is transformed into ordinary by the utilization of similarity rules and a numerical technique is adapted for the solution. Interval type-2 trapezoidal fuzzy sets are used in this fuzzy analysis to investigate the role of several physical factors on velocity and temperature distribution, shear rate, Nusselt number (rate of heat transfer), nanoparticle diameter, fluid temperature, and volume concentration. The outcomes, which show these parameters affect the flow behavior, are displayed as tables and graphs. The main conclusions show that Brownian conductivity is strongly enhanced by fluid temperature and diminishes with increasing particle diameter. Furthermore, raising the volume concentration of nanoparticles tends to lower fluid temperature, which speeds up cooling procedures and is beneficial for the manufacturing of industrial materials.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101086"},"PeriodicalIF":0.0,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Radiation effects on rotating system free convective nanofluid unsteady flow with heat source and magnetic field","authors":"Manjunatha N ,&nbsp;M.Girinath Reddy ,&nbsp;Ahmad Aloqaily ,&nbsp;Sarah Aljohani ,&nbsp;A.Rupesh Reddy ,&nbsp;Farhan Ali ,&nbsp;Nabil Mlaiki","doi":"10.1016/j.padiff.2025.101083","DOIUrl":"10.1016/j.padiff.2025.101083","url":null,"abstract":"<div><div>The analytical investigation delves into the intricate interplay between radiation, magnetic fields, and convective nanofluid flow within a rotating system that is subject to a heat source. The velocity along the plate is postulated to undergo oscillatory motion in the temporal domain, exhibiting a uniform frequency. In this particular experimental setup, the base fluids under consideration are water (H₂O) and ethylene glycol (C₂H₆O₂), while the nanoparticles being investigated consist of copper (Cu), titanium (TiO₂), silver (Ag), and alumina (Al₂O₃). The analytical outcomes of the equations are derived through the utilization of perturbation methodology. The analysis and depiction of the impacts of the distinct factors are elucidated and visually represented in graphical form. The analytical discussions are undertaken to explore the impact of nanoparticles in the presence of radiation and rotating fluid on velocity, temperature profiles, skin friction coefficient, and Nusselt number. One observes the fluctuations in the velocity and thermal curves concerning various relevant physical parameters. The augmentation of the mass transpiration (suction) parameter intensity leads to an amplification in skin friction, thereby resulting in an enrichment of thermal transmission and a reduction in the temperature of the nanofluid. Moreover, it is demonstrated that the skin friction coefficient exhibits an augmentation as a consequence of mass suction and magnetic field, while concurrently witnessing decay in the thermal transmission rate.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101083"},"PeriodicalIF":0.0,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A fractional-order model of the dynamics of the electorate in a multi-party democracy","authors":"Binandam Stephen Lassong ,&nbsp;Shaibu Osman ,&nbsp;Christian John Etwire","doi":"10.1016/j.padiff.2024.101055","DOIUrl":"10.1016/j.padiff.2024.101055","url":null,"abstract":"<div><div>The complexity of real-world problems has led to the development of fractional differential operators, a groundbreaking mathematical tool that overcomes the limitations of classical calculus. This article proposes an ABC fractional derivative model to analyze the dynamics of the electorate in multiparty democracies. The ABC fractional derivatives, characterized by their non-local and non-singular kernels, facilitate a deeper understanding of the crossover behavior in the model, yielding valuable insights into the complex underlying dynamics. The properties of the Atangana–Baleanu operator are explored, and the uniqueness and existence of solutions are determined. The Hyers–Ulam stability is established, and the political party reproduction is calculated. The model is validated using data from the 2020 Ghana Presidential Elections, exhibiting a crossover effect at <span><math><mrow><mi>ξ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><mo>.</mo></mrow></math></span> The fractional order operator significantly impacts all compartments, predicting an increase in votes for small parties and a decline for major parties. In particular, the findings reveal a significant increase in voters who joined political parties in the past four years. Future studies may explore optimal control strategies for multiparty democracies.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101055"},"PeriodicalIF":0.0,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analytical simulations for rate type nanomaterial stretching flow with dual convection","authors":"Manzoor Ahmad ,&nbsp;Sami Ullah Khan ,&nbsp;Syeda Quratulain ,&nbsp;Adnan ,&nbsp;M. Waqas ,&nbsp;Hakim AL Garalleh ,&nbsp;Nurnadiah Zamri ,&nbsp;Dilsora Abduvalieva ,&nbsp;Manish Gupta","doi":"10.1016/j.padiff.2025.101081","DOIUrl":"10.1016/j.padiff.2025.101081","url":null,"abstract":"<div><div>Owing to high thermal performances and stable properties, multiple applications of nanomaterials have been studied in different industrial and engineering processes. Ongoing continuous research in nanofluid suggested different applications of nanomaterials in catalysis, aerospace engineering, oil industry, various optical devices, medical imaging etc. The objective for exploring current investigation is to disclose the thermal impact of Oldroyd-B nanofluid comprising the buoyancy driven flow. The heat and mass transfer analysis is predicted with insight of Brownian motion and thermophoresis phenomenon. The flow is subject to bidirectional surface maintaining the uniform velocity. The zero-mass constraints are utilized for analyzing the flow phenomenon. The analytical treatment is suggested regarding the computations of developed system. Fundamental of thermal transport phenomenon are suggested with physical aspects. It is observed that velocity profile enhances with applications of buoyancy forces. The temperature profile reduces due to velocity ratio parameter. Current results present applications in cooling processes, thermal management devices, heating control, extrusion processes, chemical systems etc.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101081"},"PeriodicalIF":0.0,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On nonlinear coupled differential system for heat transfer in magnetized enclosure with T-shaped baffle by using machine learning","authors":"Khalil Ur Rehman ,&nbsp;Wasfi Shatanawi ,&nbsp;Lok Yian Yian","doi":"10.1016/j.padiff.2025.101078","DOIUrl":"10.1016/j.padiff.2025.101078","url":null,"abstract":"<div><div>It is well consensus among researchers that the constructing mathematical model for heat transfer problems results set of coupled nonlinear partial differential equations (PDEs) and the solution in this regard gets a challenging task. The present article contains an artificial neural network remedy to tackle nonlinear differential equations for heat transfer in an enclosure. In detail, we considered Casson fluid equipped in a semi-heated square cavity in the presence of both magnetic field and natural convection. The upper wall of the cavity is taken adiabatic and the lower wall is heated uniformly. The both right and left walls are considered cold. The flow is formulated in terms of coupled non-linear differential equations and solved for two different thermal flow fields namely baffle with heated tip and baffle with cold tip. An artificial intelligence-based neural model is developed to approximate the Nusselt number along the fin for both heated and cold tips of the T-shaped baffle. The low mean square error (MSE) values and perfect Regression values demonstrate the exceptional performance of the neural model being trained using the Levenberg-Marquardt algorithm. We found that the Nusselt number rises significantly with increasing Rayleigh numbers, especially in the vicinity of the heated baffle. This suggests increased buoyancy effects leading to improved convective heat transfer.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101078"},"PeriodicalIF":0.0,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Entropy analysis of Darcy–Forchheimer flow of couple-stress TiO2-CoFe2O4/engine oil based hybrid nanofluid between two rotating disks considering hall effect","authors":"Sk Enamul ,&nbsp;Seetalsmita Samal ,&nbsp;Surender Ontela","doi":"10.1016/j.padiff.2025.101073","DOIUrl":"10.1016/j.padiff.2025.101073","url":null,"abstract":"<div><div>This study investigates heat transfer and entropy production in Couple-Stress hybrid nanofluid flow between two spinning disks. It incorporates the Darcy–Forchheimer porous effects and the Hall effect. The hybrid nanofluid consists of titanium dioxide (<span><math><mrow><mi>T</mi><mi>i</mi><msub><mrow><mi>O</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>) and cobalt ferrite (<span><math><mrow><mi>C</mi><mi>o</mi><mi>F</mi><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math></span>) nanoparticles in the base fluid of engine oil. The governing equations are made dimensionless through similarity transformations. The semi-analytical methodology known as the homotopy analysis method (<span><math><mrow><mi>H</mi><mi>A</mi><mi>M</mi></mrow></math></span>) is then applied to the solution. Critical parameters such as the inertial coefficient, heat source parameter, nanoparticle concentration, and magnetic field parameter are analyzed graphically. These analyses explore their effects on velocity profiles, temperature distribution, and entropy generation. The findings demonstrate that radial velocity initially increases and then decreases with an increasing inertial coefficient, while axial velocity increases consistently. The temperature profile grows with a higher heat source parameter, reflecting enhanced internal heat generation. Entropy generation displays non-linear behavior concerning the heat source parameters. The Bejan number decreases near the disks due to efficient heat transfer. However, it increases in the central region, where thermal irreversibility dominates at higher values of volume fraction concentration of <span><math><mrow><mi>T</mi><mi>i</mi><msub><mrow><mi>O</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>. These results provide valuable insights into the effects of nanoparticle concentration. They also shed light on the impact of thermal characteristics and flow parameters. This study optimizes thermal management and heat transfer systems in engineering applications. It offers guidance for improving energy efficiency in advanced fluid dynamics scenarios.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101073"},"PeriodicalIF":0.0,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effect of activation energy on Casson–Maxwell fluid via porous media including blowing and suction mechanisms","authors":"J. Jayaprakash ,&nbsp;V. Govindan ,&nbsp;Haewon Byeon","doi":"10.1016/j.padiff.2024.101060","DOIUrl":"10.1016/j.padiff.2024.101060","url":null,"abstract":"<div><h3>Purpose:</h3><div>The Casson–Maxwell fluid model, when subjected to an applied magnetic field with suction, blowing, and activation energy considerations, offers a comprehensive framework for understanding and optimizing the behavior of complex fluids in various applications. By accounting for yield stress, viscoelastic properties, and temperature-dependent effects, the model enhances process design, performance optimization, and efficiency across industrial, biomedical, environmental, and energy systems.</div></div><div><h3>Design/Methodology/Approach:</h3><div>This study examines the steady flow of a Casson–Maxwell fluid over a porous stretching sheet influenced by Arrhenius activation energy, an applied magnetic field, multiple slip conditions, and surface suction and blowing effects. The analysis incorporates thermal radiation and concentration variations influenced by activation energy, chemical reactions, and multiple slip effects. This approach provides a comprehensive understanding of the complex interactions governing such systems, with relevance to applications in polymer processing, food processing, blood flow in medical devices, and drug delivery systems. Using the shooting method in Matlab, the Runge–Kutta–Fehlberg approach evaluates the convergence of the numerical solution to the governing equations.</div></div><div><h3>Findings:</h3><div>The results, illustrated through visualizations, elucidate the impact of various non-dimensional parameters including slip parameters on the boundary layers of the Casson–Maxwell fluid model under suction and injection. Parameters such as the Hartmann number, porous medium factor, Maxwell and Casson fluid parameters, Darcy number, Soret and Prandtl numbers, radiation parameter, Schmidt and Eckert numbers, chemical reaction parameter, Arrhenius activation energy parameter, and slip parameters significantly influence boundary layer behavior. The observed variations are attributed to enhanced resistive forces from the magnetic field, reduced yield stress, viscoelastic effects, and decreased shear stress at the boundary.</div></div><div><h3>Originality/values:</h3><div>This study presents a novel investigation into the effects of suction and blowing on the steady flow of a non-Newtonian Casson–Maxwell fluid over a stretched porous flat plate. By incorporating linear velocity, momentum, thermal and concentration slip conditions, solar radiation, external magnetic flux, thermal and chemical reactions, Arrhenius activation energy, and suction and blowing effects, the research explores under-examined factors in fluid dynamics. The study’s originality and relevance lie in addressing these factors, which have significant implications but have been insufficiently explored in previous research, thereby underscoring the importance of this contribution.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101060"},"PeriodicalIF":0.0,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Study of nonlinear wave equation of optical field for solotonic type results","authors":"Ikram Ullah ,&nbsp;Muhammad Bilal ,&nbsp;Dawood Shah ,&nbsp;Hasib Khan ,&nbsp;Jehad Alzabut ,&nbsp;Hisham Mohammad Alkhawar","doi":"10.1016/j.padiff.2024.101048","DOIUrl":"10.1016/j.padiff.2024.101048","url":null,"abstract":"<div><div>This paper uses the fractional perturbed Gerdjikov–Ivanov (PGI) model, a basic mathematical framework in mathematical physics and nonlinear dynamics, to examine complex wave structures using the M-fractional operator and modified Extended Direct Algebraic Method (mEDAM). We find a wide variety of new optical wave solutions, such as kink-type, dark, brilliant, periodic, combo, exponential, trigonometric, and hyperbolic solutions. our examine the dynamic behavior and free parameters of these soliton solutions using contour plots and three-dimensional charts. The uniqueness of the study is shown by the noteworthy consistency and divergence of our results from earlier answers. This work makes a substantial contribution to the PGI model’s ability to extract many solitary wave solutions. The proposed suggested method shows dependability while assessing analytical solutions for fractional differential equations. This research intends to extend mathematical approaches for solving fractional differential equations, which will enable answers to a wide range of practical scientific and engineering problems, including implications for ultrafast pulse transmission in optical fibers.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101048"},"PeriodicalIF":0.0,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fractional-order boundary value problems solutions using advanced numerical technique","authors":"Asmat Batool ,&nbsp;Imran Talib ,&nbsp;Muhammad Bilal Riaz","doi":"10.1016/j.padiff.2024.101059","DOIUrl":"10.1016/j.padiff.2024.101059","url":null,"abstract":"<div><div>The main motivation of this study is to extend the use of the operational matrices approach to solve fractional-order two-point boundary value problems (TPBVPs), a method often employed in the literature for solving fractional-order initial value problems. Our proposed approach employs innovative operational matrices, specifically the integral operational matrices based on Chelyshkov polynomials (CPs), a type of orthogonal polynomials. These operational matrices enable us to integrate monomial terms into the algorithm, effectively converting the problem into easily solvable Sylvester-type equations. We provide a comprehensive comparison to demonstrate the accuracy and computational advantages of our proposed approach against existing methods, including the exact solution, the Haar wavelet method (HWM), the Bessel collocation method (BCM), the Pseudo Spectral Method (PSM), the Generalized Adams–Bashforth–Moulton Method (GABMM) and the fractional central difference scheme (FCDS) through numerical examples. Additionally, our proposed approach is well-suited for solving problems with both polynomial and non-polynomial solutions.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101059"},"PeriodicalIF":0.0,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}