Partial Differential Equations in Applied Mathematics最新文献

{"title":"Analysis of blood flow features in the curved artery in the presence of differently shaped hybrid nanoparticles","authors":"K.N. Asha,&nbsp;Neetu Srivastava","doi":"10.1016/j.padiff.2025.101117","DOIUrl":"10.1016/j.padiff.2025.101117","url":null,"abstract":"<div><div>This study combines the analysis of blood flow in curved arteries with the exploration of how differently shaped hybrid nanoparticles impact these flows, offering potential applications in biomedical engineering, nanomedicine, and the treatment of cardiovascular diseases. The study explores how different fluid flow parameters and nanoparticle shapes affect the velocity, wall shear stress, Nusselt number and temperature profiles in a curved artery. The analytical approach is employed determine the solutions of the governing equations, leading to solutions for velocity, wall shear stress, Nusselt number, and temperature distributions, while taking into account the effects of slip at the boundary. The shape of nanoparticles affects all the velocity, wall shear stress, temperature and the Nusselt number within a stenotic curved artery. This work provides a comprehensive overview of the mathematical model, its solutions, and visual data, offering valuable insights for researchers and medical professionals on the potential applications of hybrid nanoparticles in managing stenotic blood flow.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101117"},"PeriodicalIF":0.0,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143351137","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":"Sinusoidal shear deformable beam theory for analytic nonlocal elasticity","authors":"D. Indronil","doi":"10.1016/j.padiff.2025.101116","DOIUrl":"10.1016/j.padiff.2025.101116","url":null,"abstract":"<div><div>This paper presents a unified nonlocal sinusoidal shear deformation theory to comprehensively analyze nanobeam bending, buckling, and free vibration. The proposed model effectively distinguishes bending and shear components, accurately capturing small-scale effects and transverse shear deformation without shear correction factors. The energy and governing equations were derived using Hamilton's principle and solved analytically through the Laplace Transformation method. This approach led to the exact expressions for key mechanical responses, including the displacement equation for bending, the buckling load for stability, and the frequency equation for vibration analysis. The results are extensively presented in table and graphical formats, offering a detailed study of the effects of various parameters on the behavior of nanobeams. Furthermore, the model's predictions were validated against existing beam theories, demonstrating its enhanced accuracy and robustness. This study significantly advances the understanding of nanobeam mechanics by providing a powerful and versatile framework for designing and analyzing nanoscale structures. The findings are particularly relevant for applications where precise control over mechanical properties is crucial, making this work a valuable contribution to the field of nanotechnology and advanced material engineering.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101116"},"PeriodicalIF":0.0,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419211","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 computational time integrator for heat and mass transfer modeling of boundary layer flow using fuzzy parameters","authors":"Muhammad Shoaib Arif ,&nbsp;Wasfi Shatanawi ,&nbsp;Yasir Nawaz","doi":"10.1016/j.padiff.2025.101113","DOIUrl":"10.1016/j.padiff.2025.101113","url":null,"abstract":"<div><div>Engineering and industrial applications depend on boundary layer flow, the thin fluid layer near a solid surface with significant viscosity. It is imperative to comprehend the mechanics of heat and mass transfer to enhance aeronautical technology, forecast weather, and design thermal systems that are more efficient. Modelling and simulating these flows with precision is indispensable. Numerous models presume that fluid characteristics are continuous. Viscosity and thermal conductivity are dramatically affected by pressure and temperature. Complex computational methodologies are necessary to address this issue. A computational exponential integrator is modified for solving fuzzy partial differential equations. The scheme is explicit and provides second-order accuracy in time. The space discretization is performed with the existing compact scheme with sixth-order accuracy on internal grid points. The stability and convergence of the scheme are rigorously analyzed, and the results demonstrate superior performance compared to traditional first- and second-order methods, particularly at specific time step sizes. Stability and convergence analyses show that the method provides a 15 % improvement in accuracy compared to first-order methods and a 10 % improvement over second-order methods, particularly at time step sizes of <span><math><mrow><mstyle><mi>Δ</mi></mstyle><mi>t</mi><mo>=</mo><mn>0.01</mn></mrow></math></span>. Numerical experiments validate the accuracy and efficiency of the approach, showing significant improvements in modelling the influence of uncertainty on heat and mass transfer. The Hartmann number, Eckert number, and reaction rate parameters are selected as fuzzified parameters in the dimensionless model of partial differential equations. In addition, the scheme is compared with the existing first and second orders in time. The calculated results demonstrate that it works better than these old schemes on particular time step sizes. In addition, the scheme is compared with existing first- and second-order methods in time, demonstrating a 20 % reduction in computational time for large-scale simulations. The computational framework allows flexible examination of complex fluid flow issues with uncertainty and improves simulation stability and accuracy. This method enhances scientific and engineering models by employing fuzzy logic in computational fluid dynamics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101113"},"PeriodicalIF":0.0,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143351139","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":"Nonlinear vibration analysis of cantilever beams: Analytical, numerical and experimental perspectives","authors":"Qamar Abbas ,&nbsp;Rab Nawaz ,&nbsp;Haseeb Yaqoob ,&nbsp;Hafiz Muhammad Ali ,&nbsp;Muhammad Musaddiq Jamil","doi":"10.1016/j.padiff.2025.101115","DOIUrl":"10.1016/j.padiff.2025.101115","url":null,"abstract":"<div><div>This study investigates the vibrational behavior of a mild steel cantilever beam with and without an attached end mass using experimental, numerical, analytical, and computational methods. Vibrational frequencies were determined using LABVIEW, MATLAB, and SOLIDWORKS, with analytical results derived from Euler-Bernoulli beam (EBB) theory. Experimental results closely matched MATLAB simulations, with an average percentage error of 1.44%, but showed a 14.44% deviation from analytical results due to neglected accelerometer mass. Findings highlight the importance of precise modeling, accounting for factors like damping and mass effects, to achieve accurate results. The study underscores the significance of resonant frequency identification in mitigating vibration failures in engineering systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101115"},"PeriodicalIF":0.0,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143347998","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":"Investigation of new solitary stochastic structures to the Heisenberg ferromagnetic spin chain model via a Stratonovich sense","authors":"Md. Nur Alam","doi":"10.1016/j.padiff.2025.101110","DOIUrl":"10.1016/j.padiff.2025.101110","url":null,"abstract":"<div><div>This study examines how Stratonovich integrals (SIs) affect the solutions of the Heisenberg ferromagnetic spin chain (HFSC) equation using the modified (G'/G)-expansion (MG'/GE) scheme. By using arbitrary parameters, it formulates traveling wave solutions in rational, trigonometric, and hyperbolic forms. These solutions are vital for elucidating complex phenomena in plasma physics, optical fibers, quantum mechanics, superfluids, and other fields. The research employs both Itô and Stratonovich stochastic calculus (SSC) to assess the dynamic behavior of these random solutions, providing graphical representations to effectively demonstrate these behaviors. The results offer significant insights into understanding and modeling intricate behaviors across various scientific and engineering fields, showcasing the versatility and applicability of the MG'/GE scheme for addressing complex nonlinear evolution equations (NLEEs) influenced by stochastic processes. The dynamic properties and features of these solutions are extensively examined through 3-dimensional, 2-dimensional and contour plots. These graphical representations illustrate a variety of forms, such as periodic solitons, multiple solitons, singular solitons, bright-dark solitons and solitary waves. Furthermore, we relate our mathematical findings to real-world phenomena, enhancing the depth and significance of our research. This analysis centers on how phase shifts depend on various parameters and compares these shifts with those found in exact soliton solutions. With the help of Maple, a robust computer algebra system, we generate generalized solitons and examine their dynamic behavior by exploring parameter values and their interrelations. Solitons, as localized wave phenomena, play a significant role in many areas of nonlinear science, such as quantum mechanics, plasma physics, fluid dynamics, water engineering, and optical fiber technology.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101110"},"PeriodicalIF":0.0,"publicationDate":"2025-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143194115","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":"Modeling the flow of casson nanofluid on a stretching sheet with heat transfer: A study of electric MHD and Darcy-Forchheimer effects","authors":"Hamzeh Taha Alkasasbeh","doi":"10.1016/j.padiff.2025.101109","DOIUrl":"10.1016/j.padiff.2025.101109","url":null,"abstract":"<div><div>This article investigates the flow characteristics of Casson-type nanofluid, specifically focusing on its behavior under Darcy-Forchheimer conditions over a stretching sheet with convective boundary conditions, which have significant implications across various fields, particularly in engineering and biomedical applications. Understanding this flow is crucial due to its applications in various industrial processes, such as cooling systems, material processing, and biomedical engineering, where efficient heat transfer and fluid dynamics are essential. The study primarily examines the electric magnetohydrodynamic (MHD) flow of copper oxide suspended in water, forming a Casson nanofluid. This research is significant as it contributes to the optimization of cooling techniques and enhances the performance of materials in high-temperature applications. The transformation of the governing partial differential equations (PDE) into ordinary differential equations (ODE) allows for a more manageable analytical approach, facilitating numerical solutions through MATLAB's bvp4c function. The findings reveal that pure water exhibits a greater velocity and Nusselt number compared to the copper oxide-based Casson nanofluid. Conversely, the temperature and skin friction coefficient demonstrate an inverse relationship. These insights are essential for designing more effective thermal management systems, improving energy efficiency in manufacturing processes, and advancing technologies that rely on nanofluid dynamics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101109"},"PeriodicalIF":0.0,"publicationDate":"2025-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143347996","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":"Existence and stability results in a fractional optimal control model for dengue and two-strains of salmonella typhi","authors":"Anum Aish Buhader ,&nbsp;Mujahid Abbas ,&nbsp;Mudassar Imran ,&nbsp;Andrew Omame","doi":"10.1016/j.padiff.2025.101075","DOIUrl":"10.1016/j.padiff.2025.101075","url":null,"abstract":"<div><div>Co-infection with dengue and salmonella typhi could lead to devastating consequences, and sometimes even result in deaths. This could lead to tremendous hazards not only to country’s economy but also overloading health-care centers. In this article, a fractional co-infection model for dengue, and two-strains (drug-sensitive and drug-resistant) of salmonella typhi is developed by implementing Caputo fractional derivative. Existence, uniqueness and stability of the model are proved by implementing Arzela Ascoli’s theorem, Banach fixed point theorem and Hyers-Ulam stability criteria, respectively. To control the diseases, control measures namely prevention control against dengue, <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, prevention control against drug-sensitive salmonella typhi, <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, and prevention control against drug-resistant salmonella typhi, <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>3</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, are introduced into the considered model. The optimality system for corresponding fractional optimal control problem is illustrated by employing Pontryagin’s maximum principle. The simulations of the model are performed by employing fractional Euler scheme to see the impact of control measures and fractional order on the respective diseases.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101075"},"PeriodicalIF":0.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165015","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":"Boundary layer flow of a non-Newtonian fluid over an exponentially stretching sheet with the presence of a heat source/sink","authors":"Vinod Y． ,&nbsp;K.R. Raghunatha ,&nbsp;Suma Nagendrappa Nagappanavar ,&nbsp;Nodira Nazarova ,&nbsp;Manish Gupta ,&nbsp;Sangamesh","doi":"10.1016/j.padiff.2025.101111","DOIUrl":"10.1016/j.padiff.2025.101111","url":null,"abstract":"<div><div>This study examines the magnetohydrodynamic (MHD) boundary layer flow and heat transfer of a Casson fluid, a non-Newtonian fluid, over an exponentially stretching sheet, incorporating the effects of a heat source or sink and thermal radiation. The governing equations, formulated as nonlinear partial differential equations, capture the Casson fluid's properties, magnetic field effects, and radiative heat transfer. These equations are transformed into a system of nonlinear ordinary differential equations using similarity transformations, reducing the problem to a finite domain. This finite domain is effectively solved using the Taylor wavelet method, ensuring high accuracy. Key parameters, including the magnetic field, Casson fluid, radiation, heat source/sink, and Prandtl number, are analyzed to assess their impact on velocity, temperature profiles, surface skin friction, and heat transfer rates. The results show that increasing the magnetic field reduces velocity due to Lorentz forces and raises skin friction. Higher Casson fluid parameters lower the velocity gradient at the surface, reducing skin friction. Thermal radiation enhances temperature distribution, while a heat source increases thermal boundary layer thickness and temperature. Conversely, a heat sink reduces both, improving heat transfer efficiency. The Nusselt number increases with higher Prandtl numbers and heat sink parameters, indicating enhanced heat transfer. The results align with previously published findings, validating the model. This research is significant for MHD flows of non-Newtonian fluids, with applications in polymer extrusion, metal casting, and cooling technologies. The inclusion of thermal radiation and heat source/sink effects broadens its relevance to energy-intensive systems such as nuclear reactors and thermal insulation. The study underscores the effectiveness of the Taylor wavelet method for solving complex boundary layer problems, offering a valuable framework for future research. It bridges the gap between theoretical fluid dynamics and practical heat transfer applications, providing insights for optimizing systems involving Casson fluids under thermal effects.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101111"},"PeriodicalIF":0.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143194091","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":"Semi-analytical approach for solving the mathematical model of solid-phase diffusion in electrodes: An application of modified differential transform method","authors":"Shivaranjini S,&nbsp;Neetu Srivastava","doi":"10.1016/j.padiff.2025.101107","DOIUrl":"10.1016/j.padiff.2025.101107","url":null,"abstract":"<div><div>Lithium-ion batteries (LIBs) have powered the modern world to propel electric vehicles (EVs) and renewable energy sources. These technologies demand higher efficiency and reliability, thereby providing robust mathematical methods are essential for optimizing species diffusion in lithium-ion (Li-ion) cells. However, there is a notable scarcity of literature addressing time-dependent flux boundary conditions with closed-form solutions. In this work, the solid-phase diffusion problem for thin-film and spherical electrodes is considered and tackled using the novel methods Laplace transform-based differential transform method (LT-DTM) and Laplace transform-based <span><math><mi>α</mi></math></span>-parametrized differential transform method (LT-<span><math><mi>α</mi></math></span>PDTM). The problem considered is based on Fick's second law and is represented as a partial differential equation (PDE). The modelled PDE is converted to its dimensionless form using suitable dimensionless variables. The resultant non-dimensional PDE is solved using LT-DTM and LT-<span><math><mi>α</mi></math></span>PDTM. The efficiency of the proposed methods are validated by comparison with previous studies. The results reveal that the proposed methods can analyze presented solid-phase diffusion problems by reducing computational domain size and require fewer iterations to obtain closed-form solutions. Furthermore, this work enhances the theoretical understanding of diffusion in Li-ion cells, improving their effectiveness and performance by offering powerful tools for optimizing electrochemical energy conversion and storage devices.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101107"},"PeriodicalIF":0.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143194092","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":"Investigating higher dimensional Jimbo–Miwa nonlinear dynamics through phase portraits, sensitivity, chaos and soliton behavior","authors":"Muhammad Aziz ur Rehman ,&nbsp;Muhammad Bilal Riaz ,&nbsp;Muhammad Iqbal","doi":"10.1016/j.padiff.2025.101101","DOIUrl":"10.1016/j.padiff.2025.101101","url":null,"abstract":"<div><div>The main focus of this article is on the development of new wave structures for the nonlinear (3+1)-dimensional Jimbo–Miwa equation. To solve the Jimbo–Miwa equation, a modified Khater method has been employed to generate various forms of soliton wave structures. Exact solutions to this equation are considered important for the complete understanding of the dynamics of waves in a physical model. The dynamic behavior of wave structures, including solutions for brilliant, single, dark, and periodic singular solitons, is enlightened by the obtained results. Selected solutions are plotted in both two- and three-dimensional graphs to illustrate their behavior. Furthermore, the system is converted into a planar dynamical system, and the derived solutions are examined using phase portraits to illustrate and demonstrate the theoretical results. Bifurcation and chaos theories are applied to enhance comprehension of the planar dynamical system that emerges from the examined system. Additionally, an investigation into the sensitivity of the provided model is conducted, revealing a moderate level of sensitivity and stability. These innovative concepts are utilized through symbolic computations to provide comprehensive and powerful mathematical tools for addressing various benign nonlinear problems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101101"},"PeriodicalIF":0.0,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143194093","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}