Partial Differential Equations in Applied Mathematics最新文献

{"title":"Fractional-order model for two-strain Monkeypox virus: Analytical and numerical insights with optimal control strategies","authors":"Amr Elsonbaty ,&nbsp;A. El-Mesady","doi":"10.1016/j.padiff.2025.101229","DOIUrl":"10.1016/j.padiff.2025.101229","url":null,"abstract":"<div><div>In this study, we explore the dynamics of a proposed fractional-order model for human-to-human infections with dual strain Monkeypox viruses (MPVs). In addition, a suggested optimal control measures are investigated to manage the disease outbreaks within the community, which helps achieving good health and well-being goal of Sustainable Development Goals (SDGs). First, a comprehensive analytical study of the model is introduced to examine its essential properties, including existence, uniqueness, non-negativity, and boundedness of solutions. The equilibrium points of the model are found and a thorough stability analysis is conducted for each steady state. The possible bifurcation scenarios, that can be exhibited by the model, are also explored. The basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is computed and the impacts of key parameters are examined through detailed sensitivity analysis. Then, the time-dependent control variables are employed to formulate a fractional optimal control problem (FOCP) for the present model, where Pontryagin’s maximum principle (PMP) is used to constitute the necessary optimality conditions (NOCs). Numerical experiments are carried out to validate theoretical findings and assess the biological implications of the applied control measures. The numerical results indicate that the proposed combination of control strategies can effectively minimize the infection control costs while effectively working towards eradicating the infection.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101229"},"PeriodicalIF":0.0,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170620","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":"Developing and applying cubic spline method for the solution of boundary value problems in complex physical and engineering systems","authors":"Aasma Khalid ,&nbsp;Inamul Haq ,&nbsp;Akmal Rehan ,&nbsp;M.S. Osman","doi":"10.1016/j.padiff.2025.101224","DOIUrl":"10.1016/j.padiff.2025.101224","url":null,"abstract":"<div><div>It has long been a concern of researchers to address the challenges of solving higher-order differential equations. In order to approximate 11th-order boundary value problems (BVPs), this work presents a novel numerical approach that combines decomposition techniques with polynomial and Non-Polynomial Splines of third order. The method starts with a decomposition process that breaks down 11th-order BVPs into a system of second-order BVPs, breaking the problem down into smaller, more manageable parts. First-order derivatives are approximated using finite central differences, and each second-order ordinary differential equation is solved using both spline methods. These methods improve accuracy and efficiency when handling complex BVPs by providing a thorough framework for solving high-order differential equations. Comparing numerical responses with the precise response on a variety of examples was part of the numerical evaluations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101224"},"PeriodicalIF":0.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147465","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":"Two-phase micropolar nanofluid flow in an isothermal extending porous sheet with heat radiation and chemical interaction: Numerical study","authors":"MD. Shamshuddin ,&nbsp;Fakhraldeen Gamar ,&nbsp;S.O. Salawu ,&nbsp;B. Prabhakar Reddy","doi":"10.1016/j.padiff.2025.101226","DOIUrl":"10.1016/j.padiff.2025.101226","url":null,"abstract":"<div><div>This study examines the capabilities of thermal radiation and chemical reactions on the transport of a micropolar nanofluid flow along a vertical sheet contiguous with an isothermal porous structure. Using similarity variable techniques, the partial differential equations (PDEs) which elucidate the envisioned model yield nonlinear ordinary differential equations (ODEs) in their self-similar form. The fourth-order Runge-Kutta method in combination with the shooting techniques is used to solve them. The important characteristics of the fluid speed, thermal transport, and solute profiles are explained by the graphs and friction-drag, rate of thermal and solutal portages by the tables. This analysis shows that increasing Brownian motion and thermophoresis outcomes improve the concentration profile, whereas augmenting chemical reaction rate specifications and Lewis number has shown a reverse effect. The fluid speed increased by the micropolar parameter, but the angular velocity faced opposite erudition. The modified Forchheimer and Darcy factor was initiated to improve fluid velocity. The temperature field was enlarged by radiation, Darcy term, and heat source, but it was decreased by the micropolar parameter. Further, the findings, which include a table comparing local boundary friction, heat, and mass transfer rates at different parameter values, are consistent with previous studies. These results provide predictive insights into flow patterns, temperature distribution, and fluid concentration, all of which have significant consequences for engineering efficiency.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101226"},"PeriodicalIF":0.0,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144124480","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":"Dynamics of COVID-malaria co-infection with optimal control and cost-effectiveness analysis","authors":"Shikha Saha ,&nbsp;Amit Kumar Saha ,&nbsp;Chandra Nath Podder","doi":"10.1016/j.padiff.2025.101217","DOIUrl":"10.1016/j.padiff.2025.101217","url":null,"abstract":"<div><div>Due to the geographic overlap between the distributions of COVID-19 and malaria, co-infection between these diseases is highly possible and could result in severe health issues. To understand the disease dynamics of the co-infection, a new mathematical model, which incorporates vaccination as an intervention, is formulated. Theoretical analysis suggests that both the sub-models (COVID-19-only and malaria-only sub-models) and the full model undergo backward bifurcation when their respective reproduction number is less than unity. It further suggests that in the absence of re-infection both the sub-models and the full model have a globally asymptotically stable disease free equilibrium whenever the corresponding reproduction number is less than unity. The study further reveals that malaria infection may increase the risk of COVID-19, whereas COVID-19 infection may not always increase the risk of malaria. Numerical simulation also suggests that COVID-19 fatality rate increases by approximately 5 folds due to co-infection with malaria while co-infection with COVID-19 may not have significant effect on malaria fatality rate. It again shows that malaria cases can be reduced by approximately 60% if 90% individuals use non-pharmaceutical interventions (NPIs), such as nets and repellents of 90% efficacy. Using the expression of the vaccine-induced herd immunity threshold and contour plot it is shown that at least 75% individuals should be vaccinated with a vaccine of 85% efficacy to achieve herd immunity against malaria. The study also shows that strategy C (prevention strategy for both COVID-19 and malaria) is the most cost-effective strategy to mitigate the burden of co-infection.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101217"},"PeriodicalIF":0.0,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071575","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":"A hybrid analytical method for fractional order Klein–Gordon and Burgers equations","authors":"Huda Omran Altaie ,&nbsp;Adel Rashed A. Ali ,&nbsp;Ghaith Fadhil Abbas ,&nbsp;Ali Hasan Ali","doi":"10.1016/j.padiff.2025.101220","DOIUrl":"10.1016/j.padiff.2025.101220","url":null,"abstract":"<div><div>In this study, fractional-order partial differential equations (FPDEs), specifically the Klein–Gordon equation (KGE) and the Burgers equation, are analytically solved using a modified and combined version of the Elzaki Decomposition Technique (ETADM). To assess the efficacy and robustness of the proposed approach, several examples are provided to obtain analytical and numerical results related to the KGE and the Burgers equation. Furthermore, the proposed techniques yield convergent series solutions with well-defined components, without the need for perturbation or linearization. Additionally, we compare several methods for solving differential equations arising in physics and engineering, including ETADM, the Variational Iteration Method (VIM), and the Adomian Decomposition Method (ADM). For comparison and validation, three examples are presented, along with the results obtained using both ETADM and VIM.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101220"},"PeriodicalIF":0.0,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948222","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":"Cross-diffusion effects of viscous heating hydromagnetic Casson fluid flow in permeable vertical media with radiation and heat loss","authors":"B. Prabhakar Reddy ,&nbsp;MD. Shamshuddin ,&nbsp;S.O. Salawu ,&nbsp;M. Paul Matao","doi":"10.1016/j.padiff.2025.101225","DOIUrl":"10.1016/j.padiff.2025.101225","url":null,"abstract":"<div><div>This investigation is on Casson fluid transport's cross-diffusion and thermal dissipation along an oscillatory semi-infinite vertical geometry and the angled magnetic field. The study's novelty lies in the simultaneous consideration of viscous heating, cross-diffusion, and hydromagnetic effects in a Casson fluid model with heat loss an aspect scarcely addressed in previous studies. This research provides a comprehensive framework for understanding complex thermal-fluid interactions in industrial applications such as polymer processing, geothermal energy systems, and porous media heat exchangers. The complex partial differential equations (PDEs) system is converted into highly non-linear PDEs via non-dimensionalization variables. The nonlinear differential equations are solved by the numerical technique finite difference method (FDM) with suitable conditions. The flow, thermal, and concentration fields are examined for the obtained physical terms via graphical illustration. The skin friction, temperature, and mass gradients are evaluated graphically at the plate surface. As noticed, the temperature and mass buoyancy forces raised the stream rate field, but the Casson parameters have shown the opposite influence. The skin friction is strengthened by the porosity parameter but decreased with magnetic field and thermal and mass buoyancy forces. The viscous dissipation, heat absorption, and Dufour effects raised the heat gradient. The mass gradient is boosted with the Soret number, and the chemical reaction exposed the opposite trend. Finally, the investigation outcomes are meticulously verified with formerly reported results in an asymptotic situation.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101225"},"PeriodicalIF":0.0,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144083690","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 classification of group invariant solutions of the Barenblatt–Gilman model by a one-dimensional system of subalgebras","authors":"Akhtar Hussain,&nbsp;M. Usman","doi":"10.1016/j.padiff.2025.101176","DOIUrl":"10.1016/j.padiff.2025.101176","url":null,"abstract":"<div><div>The Barenblatt–Gilman (BG) equation, which simulates nonequilibrium countercurrent capillary impregnation, is discussed in this study. By applying symmetry classification to the nonlinear function <span><math><mrow><mi>Φ</mi><mrow><mo>(</mo><mi>σ</mi><mo>)</mo></mrow></mrow></math></span>, six distinct cases emerge. In the general case, <span><math><mrow><mi>Φ</mi><mrow><mo>(</mo><mi>σ</mi><mo>)</mo></mrow></mrow></math></span> yields a three-dimensional principal algebra. The other cases extend this Lie algebra to infinite dimensions, which are then reformulated as six-dimensional Lie algebras. For each of these six possible Lie algebras, a system of one-dimensional subalgebras is derived using P. Olver’s method. Group invariant solutions are obtained by performing symmetry reductions under the derived optimal system. The conservation laws of this model are determined using the direct (multiplier) approach. First, the multipliers based on dependent and independent variables are determined and after that, conserved vectors are constructed to correspond to these multipliers. This study presents analytical results in the form of invariant solutions, which are novel due to the nonlinearity of the function <span><math><mrow><mi>Φ</mi><mrow><mo>(</mo><mi>σ</mi><mo>)</mo></mrow></mrow></math></span>. Since very few analytical methods address such nonlinear problems, these solutions offer unique insights. Researchers focusing on numerical solutions can also utilize these results for comparative analysis.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101176"},"PeriodicalIF":0.0,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143935923","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":"A fractional order model of Lymphatic Filariasis and Visceral Leishmaniasis coinfection","authors":"Isaac Kwasi Adu ,&nbsp;Fredrick Asenso Wireko ,&nbsp;Joshua Nii Martey ,&nbsp;Joshua Kiddy K. Asamoah","doi":"10.1016/j.padiff.2025.101204","DOIUrl":"10.1016/j.padiff.2025.101204","url":null,"abstract":"<div><div>Lymphatic filariasis and visceral leishmaniasis are parasitic diseases that cause serious public health issues, especially in tropical and subtropical areas. Effective disease control requires an understanding of their co-infection dynamics. In this study, we construct a fractional-order model to analyze the transmission patterns of lymphatic filariasis and visceral leishmaniasis co-infection. The existence and uniqueness of the model’s solution were confirmed by using the fixed point theory; in addition, the model was proven to be positive and bounded. The stability of the fractional coinfection model is proven using the Hyers–Ulam and Hyers–Ulam–Rassias stability procedures. Sensitivity analysis was conducted using the Latin hypercube sampling technique and partial rank correlation coefficient with 10,000 runs using the reproduction number for lymphatic filariasis and visceral leishmaniasis as the response functions per time. It was observed that the parameters that had a significant influence on the spread of the diseases were <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span>, thus, the biting rates of mosquitoes and sandflies respectively, the progression rate of lymphatic filariasis in mosquitoes <span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>, the progression rate of visceral leishmaniasis in sandflies <span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span>, the progression rate of lymphatic filariasis in humans <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> and the progression rate of visceral leishmaniasis in humans and reservoirs <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span>. Therefore, policymakers are encouraged to focus on reducing the occurrence of these parameters and also use these results as a guide in developing control strategies to mitigate the spread of both disease in the population. We also observed that memory significantly impacts the dynamics of the population’s transmission patterns of lymphatic filariasis and visceral leishmaniasis co-infection.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101204"},"PeriodicalIF":0.0,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143935924","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":"Existence of ground state solutions for a class of bi-non-local Kirchhoff-type problems with variable exponents","authors":"Hind Bouaam ,&nbsp;Mohamed El Ouaarabi ,&nbsp;Said Melliani ,&nbsp;Maria Alessandra Ragusa","doi":"10.1016/j.padiff.2025.101201","DOIUrl":"10.1016/j.padiff.2025.101201","url":null,"abstract":"<div><div>Our goal in this work is to investigate the existence of ground state solutions, i.e., solutions with the least energy, for a bi-nonlocal Kirchhoff-type problem with variable exponents on compact Riemannian manifolds. Using a minimization argument combined with a quantitative deformation lemma and Brouwer degree theory, we establish the existence of solutions for the problem under consideration.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101201"},"PeriodicalIF":0.0,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948221","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":"A better iterative algorithm for fixed-point problem in Banach spaces with application","authors":"Wakeel Ahmed ,&nbsp;Shahid Zaman ,&nbsp;Tamseela Ashraf ,&nbsp;Asma Raza","doi":"10.1016/j.padiff.2025.101175","DOIUrl":"10.1016/j.padiff.2025.101175","url":null,"abstract":"<div><div>In this research article, we explore convergence results within the framework of Banach spaces by focusing on a specific iterative scheme, namely the T-iterative algorithm (TIA). Utilizing the Chatterjea–Suzuki-C (CSC) condition, we establish both strong and weak convergence. To validate the efficacy of our proposed iterative schemes, we conduct numerical experiments using MATLAB R2021a, demonstrating that our approach achieves a faster rate of convergence compared to existing methods. Furthermore, we give a clear example of complete mappings that satisfy the CSC condition whose fixed point is unique. As a practical application, we apply the main results to solve functional and fractional differential equations (FDEs), illustrating the broader applicability of our findings.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101175"},"PeriodicalIF":0.0,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143935922","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}