{"title":"Investigation of lump, breather and multi solitonic wave solutions to fractional nonlinear dynamical model with stability analysis","authors":"","doi":"10.1016/j.padiff.2024.100955","DOIUrl":"10.1016/j.padiff.2024.100955","url":null,"abstract":"<div><div>In the current research, the new extended direct algebraic method (NEDAM) and the symbolic computational method, along with different test functions, the Hirota bilinear method, are capitalized to secure soliton and lump solutions to the <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional fractional telecommunication system. Consequently, we derive soliton solutions with sophisticated structures, such as mixed trigonometric, rational, hyperbolic, unique, periodic, dark-bright, bright-dark, and hyperbolic. We also developed a lump-type solution that includes rogue waves and breathers for curiosity’s intellect. These features are important for controlling extreme occurrences in optical communications. Additionally, we investigate modulation instability (MI) in the context of nonlinear optical fibres. Understanding MI is essential for developing systems that may either capitalize on its positive features or mitigate its adverse effects. Also, a comprehensive sensitivity analysis of the observed model is carried out to evaluate the influence of different factors. 3D surfaces and 2D visuals, contours, and density plots of the outcomes are represented with the help of a computer application. Our findings demonstrate the potential of using soliton theory and advanced nonlinear analysis methods to enhance the performance of telecommunication systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445214","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":"An iterative approach for addressing monotone inclusion and fixed point problems with generalized demimetric mappings","authors":"","doi":"10.1016/j.padiff.2024.100953","DOIUrl":"10.1016/j.padiff.2024.100953","url":null,"abstract":"<div><div>Throughout this study, we present a new algorithm for finding the common solution of a finite family of monotone inclusion and the fixed point problem of a finite family of generalized demimetric operators in the context of a real Hilbert space and show its strong convergence. Moreover, we utilize our result to solve the minimization problem.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142437666","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 modifications of natural transform iterative method and q-homotopy analysis method applied to fractional order KDV-Burger and Sawada–Kotera equations","authors":"","doi":"10.1016/j.padiff.2024.100950","DOIUrl":"10.1016/j.padiff.2024.100950","url":null,"abstract":"<div><div>This manuscript presents enhanced versions of two methods: the natural transform iterative method (NTIM) and the q-homotopy analysis method (q-HAM). These methods harness concepts from Fractional Calculus, particularly leveraging the Caputo fractional derivative operator, to successfully manage the complexities of fractional-order systems. To validate their accuracy and efficiency, we applied the proposed techniques to FPDEs like the fractional-order KDV-Burger and fifth-order Sawada–Kotera equations. Our outcomes, which closely resemble the exact solutions, demonstrate how useful NTIM and q-HAM are for solving difficult FPDEs and improving the study of fractional calculus.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142442531","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, stability and the number of two-dimensional invariant manifolds for the convective Cahn–Hilliard equation","authors":"","doi":"10.1016/j.padiff.2024.100946","DOIUrl":"10.1016/j.padiff.2024.100946","url":null,"abstract":"<div><div>We study the well-known generalised version of the nonlinear Cahn–Hilliard evolution equation, supplemented with periodic boundary conditions. We study local bifurcations in the vicinity of spatially homogeneous equilibrium states. We show the possibility of the existence of a finite or countable set of equilibrium states of the boundary value problem under study, in the vicinity of which, if appropriate conditions are met, there exist two-dimensional invariant manifolds filled with solutions that are periodic in the evolutionary variable. Moreover, we derive asymptotic formulas for these periodic solutions. Finally, we study the stability of invariant manifolds and the solutions belonging to them.</div><div>In order to analyse the bifurcation problem, we used methods from the theory of dynamical systems with infinite-dimensional phase, namely the method of invariant manifolds and the method of normal forms.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142437667","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 two-strain COVID-19 co-infection model with strain 1 vaccination","authors":"","doi":"10.1016/j.padiff.2024.100945","DOIUrl":"10.1016/j.padiff.2024.100945","url":null,"abstract":"<div><div>COVID-19 has caused substantial morbidity and mortality worldwide. Previous models of strain 1 vaccination with re-infection when vaccinated, as well as infection with strain 2 did not consider co-infected classes. To fill this gap, a two co-circulating COVID-19 strains model with strain 1 vaccination, and co-infected is formulated and theoretically analyzed. Sufficient conditions for the stability of the disease-free equilibrium and single-strain 1 and -strain 2 endemic equilibria are obtained. Results show as expected that (1) co-infected classes play a role in the transmission dynamics of the disease (2) a high efficacy vaccine could effectively help mitigate the spread of co-infection with both strain 1 and 2 compared to the low-efficacy vaccine. Sensitivity analysis reveals that the main drivers of the effective reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>e</mi></mrow></msub></math></span> are primarily the effective contact rate for strain 2 (<span><math><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>), the strain 2 recovery rate (<span><math><msub><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>), and the vaccine efficacy or infection reduction due to the vaccine (<span><math><mi>η</mi></math></span>). Thus, implementing intervention measures to mitigate the spread of COVID-19 should not ignore the co-infected individuals who can potentially spread both strains of the disease.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434015","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 boundary layer flow of a Jeffrey fluid over a stretching or shrinking sheet immersed in a porous medium","authors":"","doi":"10.1016/j.padiff.2024.100951","DOIUrl":"10.1016/j.padiff.2024.100951","url":null,"abstract":"<div><div>Heat transfer optimization is critical in many applications, such as heat exchangers, electric coolers, solar collectors, and nuclear reactors. The current work looks at the thermohydraulic behavior of Jeffery fluid flow along a plane containing a magnetic field, a non-uniform heat source/sink, and a porous media. Numerical solutions are derived using the Runge-Kutta 4th-order approach and the shooting method. Graphs show how Prandtl number (Pr), thermal stratification (e<sub>1</sub>), Jeffery parameter (λ<sub>1</sub>), porous parameter (λ<sub>2</sub>), magnetic field (M), and heat generation/absorption (γ, a, b) affect velocity and temperature profiles. The results show that thermal stratification increases fluid velocity and temperature, whereas heat source/sink parameters have the reverse effect on heat transfer, and raising the Jeffrey parameter reduces velocity and increases boundary layer thickness. There is extremely high agreement with experimental data from the literature. This work illustrates the utility of hydromagnetic properties in modelling fluid flow over stretching/shrinking sheets in porous media.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419543","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 new solution approach to proportion delayed and heat like fractional partial differential equations","authors":"","doi":"10.1016/j.padiff.2024.100948","DOIUrl":"10.1016/j.padiff.2024.100948","url":null,"abstract":"<div><div>The importance of fractional partial differential equations (FPDEs) may be observed in many fields of science and engineering. On the same hand their solutions and the approaches for the same are also very important to notice due to the effectiveness of the methods and accuracy of the results. This work discusses the diverse estimated analytic description of fractional partial differential equations (with proportion delay and heat like equation), applying the Iterative Laplace Transform Method. The specified method represents a significant advancement in the tool case of applied mathematicians and scientists. Its ability to efficiently and accurately solve complex differential equations, especially FPDEs. Here in this work, the solution of four test problems of FPDEs related to proportion delay and heat like equations is obtained for testing the validity and asset of the Iterative Laplace Transform Method. Further their numerical and graphical interpretations are also mentioned.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419540","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":"Optimal control strategies for infectious disease management: Integrating differential game theory with the SEIR model","authors":"","doi":"10.1016/j.padiff.2024.100943","DOIUrl":"10.1016/j.padiff.2024.100943","url":null,"abstract":"<div><div>The rapid spread of infectious diseases poses a critical threat to global public health. Traditional frameworks, such as the Susceptible–Exposed–Infectious–Recovered (SEIR) model, have been crucial in elucidating disease dynamics. Nonetheless, these models frequently overlook the strategic interactions between public health authorities and individuals. This research extends the classic SEIR model by incorporating differential game theory to analyze optimal control strategies. By modeling the conflicting objectives of public health authorities aiming to minimize infection rates and intervention costs, and individuals seeking to reduce their infection risk and inconvenience, we derive a Nash equilibrium that provides a balanced approach to disease management. Using Picard’s iterative method, we solve the extended model to determine dynamic, optimal control strategies, revealing oscillatory behavior in public health interventions and individual preventive measures. This comprehensive approach offers valuable insights into the dynamic interactions essential for effective infectious disease control.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419617","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":"Numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion-wave equations","authors":"","doi":"10.1016/j.padiff.2024.100947","DOIUrl":"10.1016/j.padiff.2024.100947","url":null,"abstract":"<div><div>In the current study, we solve two very important mathematical models, such as the time fractional-order space-fractional telegraph and diffusion-wave equations using a reliable technique called the Adomian decomposition natural method (ADNM), which combines Adomian decomposition and natural transform. The diffusion wave equation describes the flood wave propagation, which is used in solving overland and open channel flow problems. For this reason, it is critical to fully understand and effectively solve the diffusion wave equations. Because telegraph equations are crucial for modeling and developing voltage or frequency transmission, they are widely used in physics and engineering. Furthermore, the designing process is greatly impacted by the uncertainty in the system parameters. For nonlinear ordinary differential equations based on the theorem of Banach fixed point, we provide existence and uniqueness theorem proofs. The present approach has been successfully used to explore exact solutions for time fractional-order and space fractional-order applications. The results show how effective and valuable the ADNM. This paper presents a methodology that will be used in future work to address similar nonlinear problems related to fractional calculus.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419544","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":"Thermal analysis of hybrid nano-fluids: Modeling and non-similar solutions","authors":"","doi":"10.1016/j.padiff.2024.100944","DOIUrl":"10.1016/j.padiff.2024.100944","url":null,"abstract":"<div><div>The thermal analysis of hybrid nano-fluids is a significant research area with diverse applications in industries such as paint, electronics, and mechanical engineering. Existing literature provides limited solutions to the governing equations for the flow of these fluids. Modeling and deriving non-similar solutions for these equations pose interesting and challenging mathematical problems. This study focuses on investigating heat transfer in the flow of two types of nano-fluids, specifically Al<sub>2O<sub>3/H<sub>2O</sub></sub></sub> micropolar nano-fluid and Al<sub>2</sub>O<sub>3</sub> + Ag/H<sub>2</sub>O hybrid nano-fluid, near an isothermal sphere. Conservation laws are employed to formulate the mathematical problem, and by normalizing the variables, the governing equations are converted into a set of dimensionless partial differential equations. Non-similar solutions are then obtained using numerical methods. A comparative analysis is carried out to assess the influence of various parameters on different profiles and engineering quantities for both types of nano-fluids. Both linear and rotational velocities fall down near the surface of sphere with rising microstructure in hybrid nanofluid. The micro-rotation parameter rises the temperature profile while reduces the Nusselt number of both traditional Al<sub>2</sub>O<sub>3</sub>/water based nanofluid as well as hybrid nanofluid.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419615","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}