In this work, we have analysed the impact of a transverse magnetic field on the steady flow of an incompressible conducting couple stress fluid within a rectangular channel of uniform cross-section, incorporating suction or injection at the lateral walls. In order to get the velocity ‘w’ along the axis of the rectangular tube, we ignore the induced electric and magnetic fields. To find w, we apply the standard hyper stick and no slip boundary conditions. The velocity w and temperature θ were calculated using Fourier series. The velocity distribution compared for various magnetic parameter values by taking suction velocity zero and the results are in good agreement (99.99 %) with the existing results. The volumetric flow rate and skin friction are obtained and the effects of physical parameters like magnetic parameter, Reynolds number and couple stress parameter on this are studied through graphs.
在这项研究中，我们分析了横向磁场对不可压缩传导耦合应力流体在横截面均匀的矩形通道内稳定流动的影响，其中包括侧壁的吸力或注入力。为了得到沿矩形管轴线的速度 "w"，我们忽略了感应电场和磁场。为了求得 w，我们采用了标准的超棒和无滑移边界条件。速度 w 和温度 θ 使用傅里叶级数进行计算。在吸入速度为零的情况下，比较了不同磁参数值下的速度分布，结果与现有结果非常吻合（99.99%）。得出了体积流量和表皮摩擦力，并通过图表研究了磁参数、雷诺数和耦合应力参数等物理参数对其的影响。
{"title":"Steady flow of couple stress fluid through a rectangular channel under transverse magnetic field with suction","authors":"Pavan Kumar Reddy Muduganti , Aparna Podila , Pothanna Nalimela , Mahesh Garvandha , Venkata Ramana Murthy Josyula","doi":"10.1016/j.padiff.2024.100956","DOIUrl":"10.1016/j.padiff.2024.100956","url":null,"abstract":"<div><div>In this work, we have analysed the impact of a transverse magnetic field on the steady flow of an incompressible conducting couple stress fluid within a rectangular channel of uniform cross-section, incorporating suction or injection at the lateral walls. In order to get the velocity ‘<em>w</em>’ along the axis of the rectangular tube, we ignore the induced electric and magnetic fields. To find <em>w</em>, we apply the standard hyper stick and no slip boundary conditions. The velocity <em>w</em> and temperature <em>θ</em> were calculated using Fourier series. The velocity distribution compared for various magnetic parameter values by taking suction velocity zero and the results are in good agreement (99.99 %) with the existing results. The volumetric flow rate and skin friction are obtained and the effects of physical parameters like magnetic parameter, Reynolds number and couple stress parameter on this are studied through graphs.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100956"},"PeriodicalIF":0.0,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529093","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}
Pub Date : 2024-10-09DOI: 10.1016/j.padiff.2024.100946
A.N. Kulikov, D.A. Kulikov
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.
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.
{"title":"Existence, stability and the number of two-dimensional invariant manifolds for the convective Cahn–Hilliard equation","authors":"A.N. Kulikov, D.A. Kulikov","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":"12 ","pages":"Article 100946"},"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}
Pub Date : 2024-10-09DOI: 10.1016/j.padiff.2024.100945
Taqi A.M. Shatnawi , Stephane Y. Tchoumi , Herieth Rwezaura , Khalid Dib , Jean M. Tchuenche , Mo’tassem Al-arydah
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 are primarily the effective contact rate for strain 2 (), the strain 2 recovery rate (), and the vaccine efficacy or infection reduction due to the vaccine (). 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.
{"title":"A two-strain COVID-19 co-infection model with strain 1 vaccination","authors":"Taqi A.M. Shatnawi , Stephane Y. Tchoumi , Herieth Rwezaura , Khalid Dib , Jean M. Tchuenche , Mo’tassem Al-arydah","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":"12 ","pages":"Article 100945"},"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}
Pub Date : 2024-10-06DOI: 10.1016/j.padiff.2024.100951
Nagaraju B , N Kishan , Jagadish V. Tawade , Pandikani Meenapandi , Barno Abdullaeva , M. Waqas , Manish Gupta , Nadia Batool , Furqan Ahmad
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 (e1), Jeffery parameter (λ1), porous parameter (λ2), 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.
{"title":"Analysis of boundary layer flow of a Jeffrey fluid over a stretching or shrinking sheet immersed in a porous medium","authors":"Nagaraju B , N Kishan , Jagadish V. Tawade , Pandikani Meenapandi , Barno Abdullaeva , M. Waqas , Manish Gupta , Nadia Batool , Furqan Ahmad","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":"12 ","pages":"Article 100951"},"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}
Pub Date : 2024-10-05DOI: 10.1016/j.padiff.2024.100948
Alok Bhargava , D.L. Suthar , Deepika Jain
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.
{"title":"A new solution approach to proportion delayed and heat like fractional partial differential equations","authors":"Alok Bhargava , D.L. Suthar , Deepika Jain","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":"12 ","pages":"Article 100948"},"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}
Pub Date : 2024-10-04DOI: 10.1016/j.padiff.2024.100943
Awad Talal Alabdala , Yasmin Adel , Waleed Adel
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.
{"title":"Optimal control strategies for infectious disease management: Integrating differential game theory with the SEIR model","authors":"Awad Talal Alabdala , Yasmin Adel , Waleed Adel","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":"12 ","pages":"Article 100943"},"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}
Pub Date : 2024-10-03DOI: 10.1016/j.padiff.2024.100947
Nazek A. Obeidat, Mahmoud S. Rawashdeh, Malak Q. Al Erjani
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.
{"title":"Numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion-wave equations","authors":"Nazek A. Obeidat, Mahmoud S. Rawashdeh, Malak Q. Al Erjani","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":"12 ","pages":"Article 100947"},"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}
Pub Date : 2024-09-30DOI: 10.1016/j.padiff.2024.100944
A. Abbasi , W. Farooq , M. Ijaz Khan , Barno Sayfutdinovna Abdullaeva , Sami Ullah Khan , M. Waqas
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 Al2O3/H2O micropolar nano-fluid and Al2O3 + Ag/H2O 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 Al2O3/water based nanofluid as well as hybrid nanofluid.
{"title":"Thermal analysis of hybrid nano-fluids: Modeling and non-similar solutions","authors":"A. Abbasi , W. Farooq , M. Ijaz Khan , Barno Sayfutdinovna Abdullaeva , Sami Ullah Khan , M. Waqas","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":"12 ","pages":"Article 100944"},"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}
Pub Date : 2024-09-27DOI: 10.1016/j.padiff.2024.100939
S. Dhivya , V. Govindan , Choonkil Park , Siriluk Donganont
In this study, we present a novel investigation into the dynamics of the Nipah virus through the lens of fractional differential equations (FDEs), employing the Atangana–Baleanu–Caputo fractional derivative (ABCFD) and the fixed-point approach (FPA). The core contribution of this work lies in establishing the existence and uniqueness of solutions to the proposed FDEs, a critical step for validating the model. Furthermore, we explore the Hyers–Ulam (HU) stability of these generalized FDEs, providing a rigorous mathematical foundation for the stability analysis within the context of viral dynamics. By leveraging the ABCFD, our work extends the classical stability criteria, offering new insights into the role of memory effects in disease modeling. Additionally, we present approximate solutions across various compartments and fractional orders, highlighting the sensitivity of the system to key parameters. Numerical simulations, conducted using the Cullis method, illustrate the impact of fractional orders and validate the theoretical findings, positioning this work as a significant advancement in the application of fractional calculus to epidemiological models.
{"title":"Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method","authors":"S. Dhivya , V. Govindan , Choonkil Park , Siriluk Donganont","doi":"10.1016/j.padiff.2024.100939","DOIUrl":"10.1016/j.padiff.2024.100939","url":null,"abstract":"<div><div>In this study, we present a novel investigation into the dynamics of the Nipah virus through the lens of fractional differential equations (FDEs), employing the Atangana–Baleanu–Caputo fractional derivative (ABCFD) and the fixed-point approach (FPA). The core contribution of this work lies in establishing the existence and uniqueness of solutions to the proposed FDEs, a critical step for validating the model. Furthermore, we explore the Hyers–Ulam (HU) stability of these generalized FDEs, providing a rigorous mathematical foundation for the stability analysis within the context of viral dynamics. By leveraging the ABCFD, our work extends the classical stability criteria, offering new insights into the role of memory effects in disease modeling. Additionally, we present approximate solutions across various compartments and fractional orders, highlighting the sensitivity of the system to key parameters. Numerical simulations, conducted using the Cullis method, illustrate the impact of fractional orders and validate the theoretical findings, positioning this work as a significant advancement in the application of fractional calculus to epidemiological models.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100939"},"PeriodicalIF":0.0,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419616","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}
Pub Date : 2024-09-27DOI: 10.1016/j.padiff.2024.100938
M. Latha Maheswari , Karthik Muthusamy
This paper focuses on the analysis of a class of stochastic differential equations with tempered -Caputo fractional derivative (-CFD) and Lévy noise. We propose comprehensive mathematical techniques to address the existence, uniqueness and stability of solution to this equation. For existence and uniqueness, the Picard–Lindelof successive approximation technique is used analyze the results. Also, We use Mittag-Leffler (M-L) function to investigate the stability of the solution. This research applies the broad understanding of stochastic processes and fractional differential equations, as well as known results, to the analysis of systems with tempered -CFD. These equations capture complex phenomena in the field of financial assets, making their investigation on the stock prices particularly valuable.
{"title":"Dynamical behavior of tempered φ-Caputo type fractional order stochastic differential equations driven by Lévy noise","authors":"M. Latha Maheswari , Karthik Muthusamy","doi":"10.1016/j.padiff.2024.100938","DOIUrl":"10.1016/j.padiff.2024.100938","url":null,"abstract":"<div><div>This paper focuses on the analysis of a class of stochastic differential equations with tempered <span><math><mi>φ</mi></math></span>-Caputo fractional derivative (<span><math><mi>φ</mi></math></span>-CFD) and Lévy noise. We propose comprehensive mathematical techniques to address the existence, uniqueness and stability of solution to this equation. For existence and uniqueness, the Picard–Lindelof successive approximation technique is used analyze the results. Also, We use Mittag-Leffler (M-L) function to investigate the stability of the solution. This research applies the broad understanding of stochastic processes and fractional differential equations, as well as known results, to the analysis of systems with tempered <span><math><mi>φ</mi></math></span>-CFD. These equations capture complex phenomena in the field of financial assets, making their investigation on the stock prices particularly valuable.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100938"},"PeriodicalIF":0.0,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357950","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}
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