Partial Differential Equations in Applied Mathematics最新文献

{"title":"Deterministic and stochastic models for analyzing the dynamics of diabetes mellitus","authors":"Munkaila Dasumani ,&nbsp;Sianou Ezéckiel Houénafa ,&nbsp;Gohouede Lionel Cédric ,&nbsp;Binandam S. Lassong ,&nbsp;Stephen E. Moore","doi":"10.1016/j.padiff.2025.101202","DOIUrl":"10.1016/j.padiff.2025.101202","url":null,"abstract":"<div><div>Diabetes mellitus has become a global health threat as well as a financial burden. According to the International Diabetes Federation (IDF) Atlas (10th edition, 2021), approximately 537 million adults live with diabetes globally, which is anticipated to rise to 643 million in 2030 and 783 million by 2045. The report shows 6.7 million deaths due to diabetes in 2021 (1 every 5 s) and health expenditure of at least 966 billion USD (316% increase over the past 15 years). This research focuses on mathematical modeling and analysis of diabetes mellitus using deterministic and stochastic models. The study is conducted without considering genetic factors. First, we construct a deterministic diabetes mellitus model and transform it into a stochastic model by incorporating Brownian motions and stochastic environmental factor intensities. We provide qualitative results for both models, including the positivity of the solution, equilibrium points, basic reproduction numbers, local stability results, and sensitivity analysis. We show that the disease-free equilibrium is locally asymptotically stable via the Routh–Hurwitz criterion. Again, the sensitivity analysis result indicates that the transmission and birth parameters at a given period have a significant role in the increase of diabetes mellitus in the population if their values increase. We further establish the existence and uniqueness of the global positive solution by employing the random Lyapunov function theory. Using the Milstein method, the numerical scheme for the stochastic model is presented, and the approximate solution using the scheme is discussed. Additionally, we simulate the dynamics of the deterministic model using the Euler–Maruyama method. The simulation results indicate that by prioritizing policies aimed at minimizing exposure to diabetes mellitus, the strain on healthcare systems can be alleviated, leading to reduced hospitalization rates and enhanced quality of life for individuals.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101202"},"PeriodicalIF":0.0,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Anti-periodic switching dynamical system with application to chaotic system: A fixed-time fractional-order sliding mode control approach","authors":"Saim Ahmed ,&nbsp;Hasib Khan ,&nbsp;Ahmad Taher Azar ,&nbsp;Jehad Alzabut","doi":"10.1016/j.padiff.2025.101213","DOIUrl":"10.1016/j.padiff.2025.101213","url":null,"abstract":"<div><div>The paper presents an analysis of a new class anti-periodic switching dynamical system in chaotic power systems, incorporating a fixed-time control strategy. Theoretical insights, based on fixed point theorems (FPTs) and stability principles, are coupled with computational techniques to address system complexities. A robust control strategy utilizing fixed-time fractional-order sliding mode control is formulated to efficiently manage nonlinear dynamics. The Lyapunov proposition is employed to assess stability properties. The comparative analysis demonstrates the effectiveness of the approach in achieving trajectory tracking and fixed-time convergence goals. This interdisciplinary study bridges insights from chaotic power systems with control strategies, offering a valuable contribution to understanding and application in complex dynamical systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101213"},"PeriodicalIF":0.0,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigating fluctuation varieties in the propagation of the perturbed KdV equation with time-dependent perturbation coefficient","authors":"Marwan Alquran","doi":"10.1016/j.padiff.2025.101206","DOIUrl":"10.1016/j.padiff.2025.101206","url":null,"abstract":"<div><div>This study investigates the perturbed Korteweg–de Vries equation modified by incorporating time-dependent perturbation coefficient to model random fluctuations within the wave dynamics. This enhanced equation captures the probabilistic aspects of wave behavior in uncertain environments, accounting for the effects of inherent noise. The Hirota bilinear method, tanh-expansion approach, and the sine(cosine)-function method are employed to derive perturbed soliton solutions. By assigning various functional forms such as periodic, polynomial, and decaying exponential, to the proposed time-dependent coefficient, novel solitary wave patterns of types like-breather, regular(singular)-bell shaped, and periodic solutions are emerged with fluctuations. These findings are relevant for systems where environmental variability or intrinsic noise significantly affects dynamics, such as diffusion processes in physics and uncertainty behavior of water waves.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101206"},"PeriodicalIF":0.0,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143927580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy","authors":"Dilveen M. Ahmed ,&nbsp;Bewar A. Mahmood ,&nbsp;Ahmad Alalyani","doi":"10.1016/j.padiff.2025.101184","DOIUrl":"10.1016/j.padiff.2025.101184","url":null,"abstract":"<div><div>This paper addresses the numerical solution of the coupled Whitham–Broer–Kaup (WBK) problem, which has been widely investigated in engineering and physics. The WBK problem arises in various fields, including nonlinear optics, the theory of turbulence, fluid dynamics, and plasma physics. This study presents the variational homotopy perturbation method as a numerical technique for solving the coupled WBK problem. By merging the variational iteration method with the homotopy perturbation method, this approach provides accurate solutions without the need for linearization or discretization. The presented scheme is demonstrated by numerical examples that show it is easy to implement, offers superior outcomes compared to existing methods, and is both applicable and accurate. This paper introduces an improvement in numerical techniques for solving nonlinear partial differential equations, with important applications across various scientific and engineering fields.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101184"},"PeriodicalIF":0.0,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143905895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamical analysis and soliton solutions of the space–time fractional Kaup–Boussinesq system","authors":"Amjad Hussain ,&nbsp;Muhammad Hammad ,&nbsp;Ariana Abdul Rahimzai ,&nbsp;Wei Sin Koh ,&nbsp;Ilyas Khan","doi":"10.1016/j.padiff.2025.101205","DOIUrl":"10.1016/j.padiff.2025.101205","url":null,"abstract":"<div><div>This research investigates the dynamics of the fractional Kaup–Boussinesq system. Dynamical tools, such as phase portraits, bifurcation diagrams, Poincaré maps, Lyapunov exponents, and sensitivity diagrams, are employed to illustrate the system’s response to initial conditions and variations in parameters. In order to uncover the non-linear complexities of the system, a periodic forcing term is introduced, and chaotic and quasi-periodic behavior is explored. Additionally, using the extended Jacobi elliptic function technique, novel solitary wave solutions are derived, emphasizing the impact of different parameters on non-linear wave behavior. Visual representations, such as density plots and 3D graphs, further enhance the understanding of the intricate dynamics of the system.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101205"},"PeriodicalIF":0.0,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analytical and numerical investigations of slip flow in a Jeffery-Hamel configuration within a converging microchannel incorporating a step variation in wall temperature and the effects of radial heat conduction","authors":"Elhoucine Essaghir ,&nbsp;Youssef Haddout ,&nbsp;Mustapha Darif ,&nbsp;Abdelaziz Oubarra ,&nbsp;Jawad Lahjomri","doi":"10.1016/j.padiff.2025.101221","DOIUrl":"10.1016/j.padiff.2025.101221","url":null,"abstract":"<div><div>This study presents analytical and numerical solutions for steady, laminar, thermally developing slip flow through a converging microchannel of the Jeffery-Hamel family with an abrupt change in wall temperature. The analysis includes the effects, not previously explored, of radial conduction and rarefaction. The elliptic energy equation is analytically solved using functional analysis method by decomposing it into two first-order partial differential equations. Numerical validation is performed using a second-order finite difference method, showing a high agreement with a maximum deviation error &lt;0.2 %, confirming the accuracy of both methodologies in efficiently resolving the singularity. Radial conduction is influenced by the ratio of the aperture angle ψ to the Péclet number, becoming significant as this ratio increases and diminishes with higher Knudsen numbers <em>Kn</em>. Additionally, heat transfer is enhanced with a larger aperture angle but decreases with rising <em>Kn</em> due to the temperature jump at the wall. Key findings reveal optimum regime of heating characterized by a linear variation of bulk temperature and uniform heat flux, for a fixed Reynolds number and at an optimal value around ψ_<em>opt</em> = 21° in no-slip flow, decreasing to ψ_<em>opt</em> = 8.8° as the flow becomes more rarefied at <em>Kn</em> = 0.1. These insights are crucial for optimizing the thermal performance of converging microchannel flows and microfluidic device design.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101221"},"PeriodicalIF":0.0,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143935853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal control of a diffusive epidemiological model involving the Caputo–Fabrizio fractional time-derivative","authors":"Achraf Zinihi ,&nbsp;Moulay Rchid Sidi Ammi ,&nbsp;Matthias Ehrhardt","doi":"10.1016/j.padiff.2025.101188","DOIUrl":"10.1016/j.padiff.2025.101188","url":null,"abstract":"<div><div>In this work we study a fractional SEIR biological model of a reaction–diffusion, using the non-singular kernel Caputo–Fabrizio fractional derivative in the Caputo sense and employing the Laplacian operator. In our PDE model, the government seeks immunity through the vaccination program, which is considered a control variable. Our study aims to identify the ideal control pair that reduces the number of infected/infectious people and the associated vaccine and treatment costs over a limited time and space. Moreover, by using the forward–backward algorithm, the approximate results are explained by dynamic graphs to monitor the effectiveness of vaccination.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101188"},"PeriodicalIF":0.0,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comparative study of Ethylene Glycol and Fe3O4-Water on unsteady MHD fluid flow exponentially vertical accelerated plate through porous medium with radiation effect","authors":"B. Shankar Goud","doi":"10.1016/j.padiff.2025.101222","DOIUrl":"10.1016/j.padiff.2025.101222","url":null,"abstract":"<div><div>The problem of unsteady MHD flow of the nanofluids past an exponentially accelerated vertical plate embedded in a permeable medium is investigated. The three fluids are assumed to be electrically conducting water-based nanofluids. Thermal radiation and electromagnetic field impacts are taken into account. The resultant nondimensionalized boundary value problem is solved numerically using the finite difference method used in the procurement numerical results of the governing equations. The comparisons of velocity and temperature fields of Ethylene glycol-water and <em>Fe</em>₃<em>O</em>₄-Water are presented graphically. The velocity of Ethylene glycol-water is greater than that of <em>Fe</em>₃<em>O</em>₄-Water. The temperature of Ethylene glycol-water is greater than the temperature of <em>Fe</em>₃<em>O</em>₄-Water.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101222"},"PeriodicalIF":0.0,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143931671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical modeling of lumpy skin disease: New perspectives and insights","authors":"Goutam Saha ,&nbsp;Pabel Shahrear ,&nbsp;Abrar Faiyaz ,&nbsp;Amit Kumar Saha","doi":"10.1016/j.padiff.2025.101218","DOIUrl":"10.1016/j.padiff.2025.101218","url":null,"abstract":"<div><div>This research presents a new mathematical structure featuring two compartments representing cows and flies. It aims to comprehensively understand the dynamics of Lumpy Skin Disease (LSD), incorporating a temperature-dependent mortality rate for flies. We thoroughly examine the model to establish the presence of a positive solution that remains bounded. By evaluating the disease's contamination potential and inspecting the model's stability concerning both local and global equilibrium points—namely, disease-free and endemic—we calculate the reproduction number. Theoretical analysis shows that a stable disease free equilibrium co-exists with a stable endemic equilibrium whenever the basic reproduction number is less than one implying the possibility of having backward bifurcation. Numerical simulation also supports this. Furthermore, through sensitivity analysis, we explore how various model parameters affect the basic reproduction number. Our numerical investigations underscore the critical importance of regulating specific parameters, such as the disease-induced mortality rate of cows, the temperature-dependent mortality rate of flies, and the rate of transition from infected to recovered cows, in effectively managing the disease system. Numerical results also show that controlling flies population and spraying adulticide, LSD spread can be prevented.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101218"},"PeriodicalIF":0.0,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chaotic demonstration of the twin-core couplers with Kerr law non-linearity employing beta derivative","authors":"Adil Jhangeer ,&nbsp;Maham Munawar ,&nbsp;Mudassar Imran ,&nbsp;Atef Abdelkader","doi":"10.1016/j.padiff.2025.101197","DOIUrl":"10.1016/j.padiff.2025.101197","url":null,"abstract":"<div><div>The generalized auxiliary equation approach is employed to derive enhanced solitary wave solutions for nonlinear directional couplers utilizing optical metamaterials. The study highlights the influence of the fractional Beta derivative parameter on soliton dynamics, demonstrating its crucial role in shaping soliton amplitudes and wave structures. Various soliton families including semi-bright solitons, solitary dark pitched solitons, single solitons, and mixed hyperbolic, trigonometric, and rational solitons are systematically constructed. Furthermore, the impact of overlapping functions on soliton interactions is investigated, revealing their significant role in amplitude modulation, wave localization, and phase shifts. This insight provides a deeper understanding of nonlinear optical interactions and enhances the accuracy of wave propagation models in directional couplers. These solutions are further analyzed using advanced computational tools to extract numerical insights. Beyond mathematical derivations, the physical relevance of these findings is explored through phase portrait analysis, quasi-periodic patterns, Lyapunov exponents, 2D Power spectrum and 3D attractors. These analyses provide a deeper understanding of energy transfer mechanisms, stability characteristics, and nonlinear optical interactions within directional couplers. The sensitivity evaluation underscores the system’s response to perturbations, offering valuable implications for the design and optimization of optical communication systems, signal processing, and photonic device engineering.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101197"},"PeriodicalIF":0.0,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143905896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}