Partial Differential Equations in Applied Mathematics最新文献

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Fractional Calculus Approach for Variational Problems: Characterization of Sufficient Optimality Conditions and Duality
Partial Differential Equations in Applied Mathematics Pub Date : 2024-12-01 DOI: 10.1016/j.padiff.2024.100999
Ved Prakash Dubey , Devendra Kumar , Jagdev Singh , Dumitru Baleanu
{"title":"Fractional Calculus Approach for Variational Problems: Characterization of Sufficient Optimality Conditions and Duality","authors":"Ved Prakash Dubey ,&nbsp;Devendra Kumar ,&nbsp;Jagdev Singh ,&nbsp;Dumitru Baleanu","doi":"10.1016/j.padiff.2024.100999","DOIUrl":"10.1016/j.padiff.2024.100999","url":null,"abstract":"<div><div>In this paper, we present a Wolfe-type dual model containing the Caputo-Fabrizio fractional derivative, weak and strong duality results, number of Kuhn-Tucker type sufficient optimality conditions and duality results for variational problems (VPs) with Caputo-Fabrizio (CF) fractional derivative operator under weaker invexity assumptions. This newly developed fractional derivative operator delivers an exponential type kernel of nonsingular nature which characterizes the dynamics of physical systems and engineering processes with memory characteristics in a better way. This derivative operator is a convolution of first-order derivative and an exponential function. The proposed work also derives the global optimality criterion of the primal problem, Mond-Weir type duality results, and Mangasarian type strict converse duality theorem in view of this fractional differential operator possessing an exponential type kernel. The derived theorems investigate the global optimal solution of the primal problem. The main results of the present work are duality theorems and sufficient optimality conditions for VPs possessing the CF derivative. In view of applications of the derived optimality theorems, Mond-Weir type duality results have been established subjected to invexity assumptions. These applications and results generalize other important duality results of VPs and also provide results connected to duality with generalized invexity in mathematical programming. Several conventional results can also be seen as a special case of the obtained results in this work.</div></div><div><h3>2010 Mathematics Subject Classification</h3><div>90C29; 90C46; 26A33</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100999"},"PeriodicalIF":0.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142759092","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}
引用次数: 0
Numerical study of the time-fractional partial differential equations by using quartic B-spline method
Partial Differential Equations in Applied Mathematics Pub Date : 2024-12-01 DOI: 10.1016/j.padiff.2024.101008
Fahad K. Nashmi, Bushra A. Taha
{"title":"Numerical study of the time-fractional partial differential equations by using quartic B-spline method","authors":"Fahad K. Nashmi,&nbsp;Bushra A. Taha","doi":"10.1016/j.padiff.2024.101008","DOIUrl":"10.1016/j.padiff.2024.101008","url":null,"abstract":"<div><div>This paper utilizes the quartic B-spline method for the numerical resolution of time-fractional partial differential equations. The fractional Caputo derivative is employed to depict anomalous diffusion processes influenced by memory effects. The proposed numerical method utilizes quartic B-spline functions for spatial discretization and employs a finite difference method to address the time-fractional derivative. Based on the Fourier method, its stability has been evaluated to demonstrate its efficacy in addressing fractional-order models. Numerical experiments, encompassing both linear and nonlinear scenarios, are performed to illustrate the method’s effectiveness and accuracy. The results obtained are compared with exact solutions and alternative numerical methods, demonstrating improved performance in convergence and computational efficiency.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 101008"},"PeriodicalIF":0.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142759093","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}
引用次数: 0
A rational optimal block hybrid method for enhanced accuracy in solving Lane–Emden equations
Partial Differential Equations in Applied Mathematics Pub Date : 2024-12-01 DOI: 10.1016/j.padiff.2024.101003
Sandile Motsa , Salma Ahmedai , Mpho Nefale , Olumuyiwa Otegbeye
{"title":"A rational optimal block hybrid method for enhanced accuracy in solving Lane–Emden equations","authors":"Sandile Motsa ,&nbsp;Salma Ahmedai ,&nbsp;Mpho Nefale ,&nbsp;Olumuyiwa Otegbeye","doi":"10.1016/j.padiff.2024.101003","DOIUrl":"10.1016/j.padiff.2024.101003","url":null,"abstract":"<div><div>This paper introduces a block hybrid method designed for the effective resolution of Lane–Emden equations, which are characterized as second-order boundary value problems incorporating a singularity at the origin. Utilizing a strategic selection of grid points through the rational approximation of optimal points, this method aims at minimizing local truncation errors, thereby enhancing the precision of solutions. Extensive numerical experimentation reveals that this approach, hereinafter referred to as the Rational Optimal Block Hybrid Method (ROBHM), offers improved accuracy and convergence rates over traditional methods. The analysis underscores the critical role of the rational approximation parameter (denoted as <span><math><mi>d</mi></math></span>) in optimizing both accuracy and computational efficiency. By maintaining a balance between computational demands and the quality of solutions, the Rational Optimal Block Hybrid Method opens new avenues for tackling complex differential equations, thus contributing to the advancement of numerical analysis of boundary value problems marked by singularities.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 101003"},"PeriodicalIF":0.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744894","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}
引用次数: 0
Hydromagnetic blood flow through a channel of varying width bounded by porous media of finite thickness
Partial Differential Equations in Applied Mathematics Pub Date : 2024-12-01 DOI: 10.1016/j.padiff.2024.101000
K. Ramakrishnan , Furqan Ahmad , M. Waqas , Barno Abdullaeva
{"title":"Hydromagnetic blood flow through a channel of varying width bounded by porous media of finite thickness","authors":"K. Ramakrishnan ,&nbsp;Furqan Ahmad ,&nbsp;M. Waqas ,&nbsp;Barno Abdullaeva","doi":"10.1016/j.padiff.2024.101000","DOIUrl":"10.1016/j.padiff.2024.101000","url":null,"abstract":"<div><div>This study examines hydromagnetic blood flow through a channel with a varying width, bounded by porous media of finite thickness, using the Beavers–Joseph–Rudraiah slip conditions. In this context, the channel models blood flow, while the surrounding porous wall represents the tissue space. By utilizing power series approximations related to the wall slope, analytical expressions for flow characteristics including axial velocity in the x and y directions, wall momentum flux, resistance force, and shear stress are derived. These results are subsequently used to analyze blood flow through a smooth constriction surrounded by porous walls. The discussion centers on the effects of the magnetic field, slip parameter, and the width of the porous wall on flow resistance and the distribution of wall shear stress, while comparing these results with the Beavers–Joseph slip conditions. It is observed that flow resistance decreases with an increasing Hartmann number across different values of the porous parameter, which is consistent with the expectation that stronger magnetic fields reduce fluid motion and resistance. Moreover, shear stress decreases with a higher Hartmann number but increases with a larger porous parameter. Both the resistance force and shear stress are also influenced by the width of the porous walls. These findings have practical implications, particularly for evaluating the performance of prosthetic devices within the human body.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 101000"},"PeriodicalIF":0.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744892","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}
引用次数: 0
Exact solutions of line-source conduction–radiation problems via boundary tracing
Partial Differential Equations in Applied Mathematics Pub Date : 2024-12-01 DOI: 10.1016/j.padiff.2024.101009
Conway Li , Brendan J. Florio , Neville Fowkes , Miccal Matthews
{"title":"Exact solutions of line-source conduction–radiation problems via boundary tracing","authors":"Conway Li ,&nbsp;Brendan J. Florio ,&nbsp;Neville Fowkes ,&nbsp;Miccal Matthews","doi":"10.1016/j.padiff.2024.101009","DOIUrl":"10.1016/j.padiff.2024.101009","url":null,"abstract":"<div><div>Boundary tracing is a technique whereby exact solutions to boundary value problems in known domains are used to generate alternate domains admitting the same solution. Here we use line-source solutions of Laplace’s equation to produce exact solutions to the conduction–radiation problem in novel domains, such as circular regions with protrusions and teardrop-shaped regions with short or long tails. The shapes and sizes obtained are practical and could be used for novel radiator design.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 101009"},"PeriodicalIF":0.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142759094","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}
引用次数: 0
Analytical solutions to the (2+1)-dimensional cubic Klein–Gordon equation in the presence of fractional derivatives: A comparative study
Partial Differential Equations in Applied Mathematics Pub Date : 2024-12-01 DOI: 10.1016/j.padiff.2024.101001
K. M. Abdul Al Woadud , Md. Jahirul Islam , Dipankar Kumar , Aminur Rahman Khan
{"title":"Analytical solutions to the (2+1)-dimensional cubic Klein–Gordon equation in the presence of fractional derivatives: A comparative study","authors":"K. M. Abdul Al Woadud ,&nbsp;Md. Jahirul Islam ,&nbsp;Dipankar Kumar ,&nbsp;Aminur Rahman Khan","doi":"10.1016/j.padiff.2024.101001","DOIUrl":"10.1016/j.padiff.2024.101001","url":null,"abstract":"<div><div>The study seeks to obtain new analytical solutions for the (2+1)-dimensional cubic Klein–Gordon (cKG) equation using the beta derivative. By applying the unified method to the equation, various types of solitons have been generated, including periodic solitons, periodic solitons with equal and unequal wavelengths, bright solitons, and periodic singular solitons with unequal wavelengths. To demonstrate the fundamental dynamics of the soliton family, three-dimensional and two-dimensional graphs showcasing various novel solutions that satisfy the relevant equations are provided. In relation to fractionality, the bright waveform retains its overall shape, but its smoothness improves as the fractional parameters increase. Conversely, periodic wave solutions show enhanced periodicity as the fractional parameters rise. Additionally, the study provides a comprehensive comparison of solutions derived from models utilizing conformable, M-truncated, and beta derivatives. The investigation explores the effect of the fractional parameter on soliton amplitude, using graphs to illustrate this impact by assigning specific values to the fractional parameter. The properties of the waves can be modified through changes to the model's parameters to produce the appropriate wave profiles. Consequently, the solutions we obtained could be particularly valuable for analyzing physical problems associated with nonlinear complex dynamical systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 101001"},"PeriodicalIF":0.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142756879","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}
引用次数: 0
Multi-parameter-based Box–Behnken design for optimizing energy transfer rate of Darcy–Forchheimer drag and mixed convective nanofluid flow over a permeable vertical surface with activation energy
Partial Differential Equations in Applied Mathematics Pub Date : 2024-12-01 DOI: 10.1016/j.padiff.2024.101002
S.R. Mishra , Subhajit Panda , P.K. Ratha
{"title":"Multi-parameter-based Box–Behnken design for optimizing energy transfer rate of Darcy–Forchheimer drag and mixed convective nanofluid flow over a permeable vertical surface with activation energy","authors":"S.R. Mishra ,&nbsp;Subhajit Panda ,&nbsp;P.K. Ratha","doi":"10.1016/j.padiff.2024.101002","DOIUrl":"10.1016/j.padiff.2024.101002","url":null,"abstract":"<div><div>The optimization of energy transfer rate in Darcy–Forchheimer inertial drag and mixed convective nanofluid motion over a vertical permeable surface with Arrhenius kinetics is obtained by utilizing a multi-parameter-based Box–Behnken design. The proposed investigation aims to enhance thermal management systems, with a particular focus on advanced cooling technologies and geothermal energy extraction. Precise control of heat transfer is essential in these applications. The integration of Brownian motion and thermophoresis effects elucidate the study for the energy transfer characteristics of the nanofluid flow. The employment of the Darcy–Forchheimer drag effects in the porous medium and the mixed convection is considered for the combined influence of buoyancy and forced convection. Activation energy is incorporated for the simulation of chemical reaction that is useful in various industrial purpose. Numerical technique such as shooting-based Runge–Kutta is adopted for the solution of transmuted dimensionless equations obtained by using adequate similarity rules. A critical parametric analysis is projected for the contributing factor with a strong validation comparing with earlier study. The robust Box–Behnken design, a statistical experimental design is utilized for the exploration of the influence of multi parameters involving radiating heat, Eckert number, Brownian motion, thermophoresis, and thermal Biot number. Further, the important outcomes are; the flow through permeable surface give rise to the impact of suction enhances the fluid velocity and the stronger thermal convection with increasing thermal Biot number also favors in enhancing the heat transport phenomenon.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 101002"},"PeriodicalIF":0.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744895","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}
引用次数: 0
Comparison of hyperbolic and parabolic equations modelling buoyancy driven flow in a square cavity
Partial Differential Equations in Applied Mathematics Pub Date : 2024-12-01 DOI: 10.1016/j.padiff.2024.101007
E. Momoniat , R.S. Herbst , C. Harley
{"title":"Comparison of hyperbolic and parabolic equations modelling buoyancy driven flow in a square cavity","authors":"E. Momoniat ,&nbsp;R.S. Herbst ,&nbsp;C. Harley","doi":"10.1016/j.padiff.2024.101007","DOIUrl":"10.1016/j.padiff.2024.101007","url":null,"abstract":"<div><div>The effects of a hyperbolic and parabolic heat transfer equation on buoyancy-driven flow in a square cavity are studied. Boundary conditions where the bottom wall is hot and the side and top walls are cold are investigated. The case when the bottom and sidewalls are warm and the top wall is cold is also examined. Simulation of the flow is done using the finite element approach. An equation for the heat function is determined. The finite difference method is used to determine solutions to the heat transfer equation. We find that a hyperbolic heat transfer equation increases the magnitude of vorticity, stream function, and heat function. This suggests that hyperbolic heat transfer equations have stronger circulation and achieve a stable state sooner than parabolic heat transfer equations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 101007"},"PeriodicalIF":0.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142758925","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}
引用次数: 0
Combined buoyancy and Marangoni convective heat transport of CNT-water nanofluid in an open chamber with influence of magnetic field and isothermal solid block
Partial Differential Equations in Applied Mathematics Pub Date : 2024-12-01 DOI: 10.1016/j.padiff.2024.101005
M. Rajarathinam , N. Nithyadevi , Nizomiddin Juraev , M. Waqas , Furqan Ahmad , Manish Gupta , M. Ijaz Khan
{"title":"Combined buoyancy and Marangoni convective heat transport of CNT-water nanofluid in an open chamber with influence of magnetic field and isothermal solid block","authors":"M. Rajarathinam ,&nbsp;N. Nithyadevi ,&nbsp;Nizomiddin Juraev ,&nbsp;M. Waqas ,&nbsp;Furqan Ahmad ,&nbsp;Manish Gupta ,&nbsp;M. Ijaz Khan","doi":"10.1016/j.padiff.2024.101005","DOIUrl":"10.1016/j.padiff.2024.101005","url":null,"abstract":"<div><div>This paper proposes combined buoyancy and Marangoni convective heat phenomenon of CNT water nano-liquid in an open chamber subject to isothermal solid block and magnetic field. The Finite Volume Method (FVM) is incorporated to discretize the transport modeled expressions and are solved by SIMPLE algorithm. A comparison study made to authenticate the inspiration of Marangoni convection, magnetic field and isothermal block with the former literatures and shows the reliable agreement. This study scrutinizes the impact of different parameters such as Rayleigh number, Hartmann number, Marangoni number and the nanoparticles concentration. The computational result of the present analysis is deliberated with the graphical representation of streamlines, isotherms contour, velocity fields and average Nusselt number. The overall heat transport rate of the chamber is greatly improved by the rising values of Ra and ϕ but follows a decreasing trend with Ha.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 101005"},"PeriodicalIF":0.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744891","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}
引用次数: 0
Application of the Atangana–Baleanu operator in Caputo sense for numerical solutions of the time-fractional Burgers–Fisher equation using finite difference approaches
Partial Differential Equations in Applied Mathematics Pub Date : 2024-12-01 DOI: 10.1016/j.padiff.2024.100998
Shashikant Waghule , Dinkar Patil , Amjad Shaikh , Kottakkaran Sooppy Nisar
{"title":"Application of the Atangana–Baleanu operator in Caputo sense for numerical solutions of the time-fractional Burgers–Fisher equation using finite difference approaches","authors":"Shashikant Waghule ,&nbsp;Dinkar Patil ,&nbsp;Amjad Shaikh ,&nbsp;Kottakkaran Sooppy Nisar","doi":"10.1016/j.padiff.2024.100998","DOIUrl":"10.1016/j.padiff.2024.100998","url":null,"abstract":"<div><div>This research investigates the numerical solution of the time-fractional Burgers–Fisher equation, utilizing the Atangana–Baleanu differential operator in the Caputo sense. This study addresses the need to comprehend the dynamics of nonlinear phenomena encountered in various scientific and engineering contexts, specifically within the Burgers–Fisher equation, which intertwines diffusion and reaction processes. Our findings reveal that the application of the Atangana–Baleanu operator significantly alters the behavior of the system, exhibiting distinct characteristics compared to traditional methods. Notably, we identify unique patterns of propagation, such as enhanced wave speed and altered front dynamics, that emerge due to the fractional dynamics. The simulations demonstrate improved stability and convergence properties when utilizing the Atangana–Baleanu operator, allowing for more accurate representations of physical processes. Additionally, we observe the emergence of non-local effects and the potential for multiple equilibrium states, enriching our understanding of the complex interactions within the system. Through the finite difference method, we efficiently discretize the continuous problem, facilitating simulations that illustrate the intricate temporal behavior of the time-fractional system. This methodology not only enhances the understanding of the physical processes involved but also contributes a novel framework for studying time-fractional equations, emphasizing the rich dynamics introduced by the Atangana–Baleanu operator in conjunction with the Caputo fractional derivative.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100998"},"PeriodicalIF":0.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744893","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}
引用次数: 0
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