Partial Differential Equations in Applied Mathematics最新文献

{"title":"Quantum-assisted hλ-adaptive finite element method","authors":"R.H. Drebotiy,&nbsp;H.A. Shynkarenko","doi":"10.1016/j.padiff.2025.101120","DOIUrl":"10.1016/j.padiff.2025.101120","url":null,"abstract":"<div><div>Quantum computing is a rapidly advancing field, driven by the potential advantages derived from the unique properties of quantum entanglement. In particular, the exponential speedup of certain carefully designed algorithms, compared to their classical counterparts, promises to significantly enhance the numerical solution of a wide range of problems.</div><div>This paper investigates the integration of quantum computing with the finite element method, focusing on singularly perturbed advection-diffusion-reaction problems. We introduce a novel finite element scheme that combines classical and quantum algorithms. In this approach, the primary mesh adaptation loop is managed by a classical computer, while a specific stabilization procedure is executed on a quantum computer. This procedure leverages the Harrow-Hassidim-Lloyd algorithm in conjunction with the swap test to estimate the value of a linear functional, which constitutes a substantial portion of the computational workload.</div><div>We demonstrate that this hybrid approach effectively eliminates parasitic oscillations in the finite element approximation, even at the early stages of the adaptation process. This leads to a significant improvement in the quality of intermediate finite element solutions. As a result, our scheme offers more efficient feedback with reduced computational costs for researchers using the method to investigate physical phenomena. To support the scheme, we prove special explicit a posteriori error estimates. Possible benefits of the proposed finite element scheme are analyzed using the numerical comparison with the typical adaptive scheme.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101120"},"PeriodicalIF":0.0,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429410","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":"Atomic solutions to Bateman–Burgers type equation via tensor products","authors":"Afaf Alhawatmeh ,&nbsp;Mohammad Al Bataineh ,&nbsp;Naba Alashqar ,&nbsp;Roshdi Khalil","doi":"10.1016/j.padiff.2025.101102","DOIUrl":"10.1016/j.padiff.2025.101102","url":null,"abstract":"<div><div>This study presents a novel approach for solving fractional partial differential equations, notably the fractional Bateman–Burgers type equation, by employing the tensor product of Banach spaces. This study proposes a novel analytical method that transcends traditional techniques like separation of variables, enabling precise atomic solutions to complex fractional equations. Central to our approach is the utilization of the <span><math><mi>α</mi></math></span>-conformable fractional derivative, which enhances the analytical framework for addressing such complex equations. Our findings provide solutions to the fractional Bateman–Burgers type equation and illustrate the potential of integrating advanced mathematical theories to solve complex problems across various scientific disciplines. This work promises to pave new pathways for research in fractional calculus and its application in both theoretical and applied mathematics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101102"},"PeriodicalIF":0.0,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387146","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":"Haar wavelet Arctic Puffin optimization method (HWAPOM): Application to logistic models with fractal-fractional Caputo-Fabrizio operator","authors":"Najeeb Alam Khan ,&nbsp;Sahar Altaf ,&nbsp;Nadeem Alam Khan ,&nbsp;Muhammad Ayaz","doi":"10.1016/j.padiff.2025.101114","DOIUrl":"10.1016/j.padiff.2025.101114","url":null,"abstract":"<div><div>This study introduces a novel hybrid numerical methodology for approximating differential equations involving the fractal-fractional Caputo-Fabrizio (FFCF) operator, which is an essential tool for modelling complex dynamical systems involving memory effects. The proposed method integrates the Haar wavelet with the Arctic Puffin optimization (APO) algorithm, a meta-heuristic optimization inspired by the foraging behavior of Arctic Puffins. The Haar wavelet, well-known for its compact support and piecewise constant characteristics, is based on the Haar basis functions used to construct an operational matrix for the FFCF operator. These matrices transform the differential equations into a system of algebraic equations involving unknown coefficients, and then optimize them using the APO algorithm, ensuring efficient and accurate solutions. Two nonlinear quadratic and cubic logistic models were examined to demonstrate the effectiveness of this method. The accuracy of the designed method was validated by comparing its results with those obtained using the modified Homotopy Perturbation method (MHPM). Error metrics, such as mean absolute error, maximum absolute error, and the experimental convergence rate, are calculated at various collocation points and presented in a tabular format. The findings revealed the method's high accuracy, rapid convergence, and computational efficiency. Overall, the proposed method offers a powerful tool for solving complex differential equations, as evidenced by its strong agreement with MHPM results. The study results were further reinforced through statistical performance metrics and their visual representations, confirming the reliability of the method, low computational cost, and its potential for broad application in numerical computations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101114"},"PeriodicalIF":0.0,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429415","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":"New existence results on random nonlocal fractional differential equation using approximating sequences","authors":"Swathi Dhandapani ,&nbsp;Ananthi Kantheeban ,&nbsp;Karthik Raja Umapathi ,&nbsp;Kottakkaran Sooppy Nisar","doi":"10.1016/j.padiff.2025.101106","DOIUrl":"10.1016/j.padiff.2025.101106","url":null,"abstract":"<div><div>In this paper, we are using approximation sequences to explore the existence and uniqueness of a particular class of random differential equations with a Caputo fractional derivative driven by colored noise. To this end, by proving Gronwall’s inequality, which contains a singular kernel as a supplementary tool to manipulate the given differential equation. Further, examples illustrate our acquired results.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101106"},"PeriodicalIF":0.0,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387144","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":"Thermo-fluid dynamics of non-newtonian casson fluid in expanding-contracting channels with joule heating and variable thermal properties","authors":"Shahid Rafiq ,&nbsp;Babar Ahmad Bilal ,&nbsp;Aysha Afzal ,&nbsp;Jagadish V. Tawade ,&nbsp;Nitiraj V. Kulkarni ,&nbsp;Barno Abdullaeva ,&nbsp;Taoufik Saidani ,&nbsp;Manish Gupta","doi":"10.1016/j.padiff.2025.101105","DOIUrl":"10.1016/j.padiff.2025.101105","url":null,"abstract":"<div><div>This study focuses on the thermo-fluid dynamics of non-Newtonian Casson fluid within a porous channel with expanding and contracting walls, a configuration of significant relevance in industrial applications like cooling systems and biomedical processes such as biofluid transport. The investigation accounts for critical factors such as Joule heating, thermal radiation, porosity, and the temperature dependence of viscosity and thermal conductivity. The governing equations are reduced to ordinary differential equations using similarity transformations and solved with the Least Square Method (LSM). The findings reveal that the Hartmann number and Eckert number strongly influence velocity and temperature profiles. Thermal radiation elevates the core fluid temperature while heat sinks reduce it near the channel walls. Viscosity models demonstrate notable effects on flow resistance and heat transfer. The findings will provide significant applications requiring efficient thermal management and precise control of fluid dynamics, making the results valuable for engineering and biomedical advancements.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101105"},"PeriodicalIF":0.0,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143194090","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 the solutions of generalized Cauchy differential equations and diffusion equations with k-Hilfer-Prabhakar derivative","authors":"Ved Prakash Dubey ,&nbsp;Jagdev Singh ,&nbsp;Sarvesh Dubey ,&nbsp;Dumitru Baleanu ,&nbsp;Devendra Kumar","doi":"10.1016/j.padiff.2025.101119","DOIUrl":"10.1016/j.padiff.2025.101119","url":null,"abstract":"<div><div>In this article, natural transform of <em>k</em>-Prabhakar integral, <em>k</em>-Prabhakar derivative, <em>k</em>-Hilfer-Prabhakar fractional derivative (<em>k</em>-HPFD) are calculated. In addition, we also obtain the natural transform of regularized versions of <em>k</em>-Prabhakar integral, <em>k</em>-Prabhakar derivative, <em>k</em>-HPFD. Finally, we solve various <em>k</em>-Hilfer-Prabhakar type Cauchy equations via operations of natural and Fourier transforms. The diffusion equations play a key role in oceanography and all models of hydrodynamics. Our new generalized solutions of <em>k</em>-HPFD type Cauchy problems and diffusion models may be used to explore fluid mechanics, ocean engineering, and wave phenomena and so on. The solutions of Cauchy equations and diffusion models considered with <em>k</em>-HPFD operator and its regularized version are computed in a shape of generalized Mittag-Leffler form by subsequent operations of integral transforms.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101119"},"PeriodicalIF":0.0,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445747","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 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}