For solving a system of nonlinear partial differential equations (PDE) emerging in an attractor one-dimensional chemotaxis model, we used a relatively new analytical method called the new modified homotopy perturbation method (NMHPM). We use NMHPM for solving one-dimensional Keller-Segel models for different types. Some properties show biologically acceptable dependency on parameter values, and numerical solutions are provided. NMHPM’s stability and reduced computing time provide it with a broader range of applications. The algorithm provides analytical approximations for different types of Keller-Segel equations. Some numerical illustrations are given to show the efficiency of the algorithm.
{"title":"Analytical Solution of One-Dimensional Keller-Segel Equations via New Homotopy Perturbation Method","authors":"Ali Slimani, Sadek Lakhlifa, A. Guesmia","doi":"10.37256/cm.5120242604","DOIUrl":"https://doi.org/10.37256/cm.5120242604","url":null,"abstract":"For solving a system of nonlinear partial differential equations (PDE) emerging in an attractor one-dimensional chemotaxis model, we used a relatively new analytical method called the new modified homotopy perturbation method (NMHPM). We use NMHPM for solving one-dimensional Keller-Segel models for different types. Some properties show biologically acceptable dependency on parameter values, and numerical solutions are provided. NMHPM’s stability and reduced computing time provide it with a broader range of applications. The algorithm provides analytical approximations for different types of Keller-Segel equations. Some numerical illustrations are given to show the efficiency of the algorithm.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140221407","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}
N. H. Mohd Razali, Lazim Abdullah, A. T. Ab Ghani, Asyraf Afthanorhan, Mojtaba Zabihinpour
Fuzzy sets are an emerging trend in shaping the development of control charts for statistical process control. The sets are germane to vague data that comes from incomplete or inaccurate measurements. Nevertheless, fuzzy sets are inadequate in some areas of industry since their membership functions are crisp numbers. The fuzzy sets are not fully able to compute higher levels of uncertainty, which might degrade the performance of the analysis. Therefore, type-2 fuzzy sets are proposed to be merged with control charts since these sets are hypothesized to be more capable of detecting a defect in process control. This paper aims to develop interval type-2 fuzzy u (IT2Fu) charts as a new approach to detecting defects. In addition, this paper presents a comparative analysis of performances between traditional u-control charts, type-1 fuzzy u-control charts, and type-2 fuzzy u-control charts. 23 samples of lubricant data with 48 subgroups were examined to identify the defects. The output showed that all of the control charts produced almost similar results except for data 14, which is “out of control” in IT2Fu-control charts but “in control” in traditional u-control charts and “rather in control” in type-1 fuzzy u-control charts. Furthermore, the performances of the charts were compared using a probability-based average run length (ARL), where probability type 1 error is computed. It was found that the ARL value of the IT2Fu-control chart showed the lowest value among the three types of charts. The analysis indicated that the IT2Fu-control chart outperformed the traditional u-control chart and the type-1 fuzzy u-control chart. The results obtained seem to support the idea that IT2Fu-control charts are more sensitive compared to type 1 fuzzy u-control charts and traditional u-control charts, so that IT2Fu-control charts are able to adequately support incomplete and vague data on process control.
模糊集是为统计过程控制制定控制图的一种新兴趋势。模糊集适用于来自不完整或不准确测量的模糊数据。然而，由于模糊集的成员函数是清晰的数字，因此在某些工业领域并不适用。模糊集不能完全计算更高层次的不确定性，这可能会降低分析的性能。因此，有人提出将 2 型模糊集与控制图合并，因为假设 2 型模糊集更能检测过程控制中的缺陷。本文旨在开发区间 2 型模糊 u (IT2Fu) 控制图，作为检测缺陷的一种新方法。此外，本文还对传统 u 控制图、1 型模糊 u 控制图和 2 型模糊 u 控制图的性能进行了比较分析。研究了 23 个润滑油数据样本，共 48 个子组，以确定缺陷。结果表明，除了数据 14 在 IT2Fu 控制图中处于 "失控 "状态，但在传统 U 控制图中处于 "受控 "状态，而在类型-1 模糊 U 控制图中处于 "相当受控 "状态之外，所有控制图都产生了几乎相似的结果。此外，还使用基于概率的平均运行长度（ARL）对图表的性能进行了比较，其中计算了概率类型 1 误差。结果发现，在三种图表中，IT2Fu 控制图的 ARL 值最低。分析表明，IT2Fu 控制图的性能优于传统 u 控制图和 1 型模糊 u 控制图。得出的结果似乎支持了这样一种观点，即 IT2Fu 控制图与 1 型模糊 U 控制图和传统 U 控制图相比更加灵敏，因此 IT2Fu 控制图能够充分支持过程控制中的不完整和模糊数据。
{"title":"A Type-2 Fuzzy u-Control Chart Considering Probability-Based Average Run Length","authors":"N. H. Mohd Razali, Lazim Abdullah, A. T. Ab Ghani, Asyraf Afthanorhan, Mojtaba Zabihinpour","doi":"10.37256/cm.5120242810","DOIUrl":"https://doi.org/10.37256/cm.5120242810","url":null,"abstract":"Fuzzy sets are an emerging trend in shaping the development of control charts for statistical process control. The sets are germane to vague data that comes from incomplete or inaccurate measurements. Nevertheless, fuzzy sets are inadequate in some areas of industry since their membership functions are crisp numbers. The fuzzy sets are not fully able to compute higher levels of uncertainty, which might degrade the performance of the analysis. Therefore, type-2 fuzzy sets are proposed to be merged with control charts since these sets are hypothesized to be more capable of detecting a defect in process control. This paper aims to develop interval type-2 fuzzy u (IT2Fu) charts as a new approach to detecting defects. In addition, this paper presents a comparative analysis of performances between traditional u-control charts, type-1 fuzzy u-control charts, and type-2 fuzzy u-control charts. 23 samples of lubricant data with 48 subgroups were examined to identify the defects. The output showed that all of the control charts produced almost similar results except for data 14, which is “out of control” in IT2Fu-control charts but “in control” in traditional u-control charts and “rather in control” in type-1 fuzzy u-control charts. Furthermore, the performances of the charts were compared using a probability-based average run length (ARL), where probability type 1 error is computed. It was found that the ARL value of the IT2Fu-control chart showed the lowest value among the three types of charts. The analysis indicated that the IT2Fu-control chart outperformed the traditional u-control chart and the type-1 fuzzy u-control chart. The results obtained seem to support the idea that IT2Fu-control charts are more sensitive compared to type 1 fuzzy u-control charts and traditional u-control charts, so that IT2Fu-control charts are able to adequately support incomplete and vague data on process control.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140241299","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}
Many epidemic diseases are season-related. Dengue is one of them. Since it is associated with a mosquito’s life cycle, it is genuinely affected by weather changes. In this paper, we model the dynamics of dengue disease transmission in the human population using two systems of delay differential equations. First, we carry out the modeling with the vertical transmission in the mosquito population and demonstrate its basic properties. Then, we implement the seasonality effect in a second model by choosing some of the parameters that are affected by weather changes to be periodically time-dependent and re-deriving these parameters. We illustrate the conditions when the disease-free periodic solution is locally asymptotically stable and when it is unstable. Simulations in this case were compatible with the theoretical results.
{"title":"Impact of Seasonality and Vertical Transmission on Mosquito Population in the Dynamics of Dengue Disease","authors":"A. Alsheri","doi":"10.37256/cm.5120243417","DOIUrl":"https://doi.org/10.37256/cm.5120243417","url":null,"abstract":"Many epidemic diseases are season-related. Dengue is one of them. Since it is associated with a mosquito’s life cycle, it is genuinely affected by weather changes. In this paper, we model the dynamics of dengue disease transmission in the human population using two systems of delay differential equations. First, we carry out the modeling with the vertical transmission in the mosquito population and demonstrate its basic properties. Then, we implement the seasonality effect in a second model by choosing some of the parameters that are affected by weather changes to be periodically time-dependent and re-deriving these parameters. We illustrate the conditions when the disease-free periodic solution is locally asymptotically stable and when it is unstable. Simulations in this case were compatible with the theoretical results.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140240375","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}
In the quest to solve the singularly perturbed delay differential equations (SPDDEs) involving large delay with integral boundary condition, the cubic spline in compression technique is explored for the study of dynamical systems to capture complex temporal phenomena in a wide range of scientific disciplines. The integral boundary condition is handled using Simpson's 1/3 rule and the scheme's applicability is validated by numerically experimenting with some problems at different values of mesh size and perturbation parameter. Numerical data are tabulated to show that the suggested approach is more accurate and is an improvement over the methods used in the literature. The insights gained from this research paper provide a foundation for further exploration and utilization of SPDDEs in understanding and predicting the behavior of complex systems across diverse scientific domains.
{"title":"Singular Perturbations and Large Time Delays Through Accelerated Spline-Based Compression Technique","authors":"Akhila Mariya Regal, Dinesh Kumar S","doi":"10.37256/cm.5120244269","DOIUrl":"https://doi.org/10.37256/cm.5120244269","url":null,"abstract":"In the quest to solve the singularly perturbed delay differential equations (SPDDEs) involving large delay with integral boundary condition, the cubic spline in compression technique is explored for the study of dynamical systems to capture complex temporal phenomena in a wide range of scientific disciplines. The integral boundary condition is handled using Simpson's 1/3 rule and the scheme's applicability is validated by numerically experimenting with some problems at different values of mesh size and perturbation parameter. Numerical data are tabulated to show that the suggested approach is more accurate and is an improvement over the methods used in the literature. The insights gained from this research paper provide a foundation for further exploration and utilization of SPDDEs in understanding and predicting the behavior of complex systems across diverse scientific domains.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140237307","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}
A. M. Mohamad Jawad, A. Biswas, Y. Yıldırım, A. Alshomrani
This paper introduces a state of the art investigation into the interaction between soliton propagation and differential group delay, offering a fresh perspective often neglected in previous studies. Motivated by the imperative to comprehend soliton behavior within inter-modal dispersion environments, it presents three innovative methodologies aimed at uncovering novel optical soliton solutions. Through the utilization of cutting-edge algorithms, these approaches unveil the emergence of solitons in hitherto unexplored contexts. The research makes significant strides through extensive numerical simulations, which not only validate theoretical conjectures but also offer practical insights. Furthermore, it delineates crucial parameter limitations essential for the existence of solitons, thus furnishing valuable guidance for future research endeavors and practical applications.
{"title":"Optical Solitons with Differential Group Delay and Inter-Modal Dispersion Singlet","authors":"A. M. Mohamad Jawad, A. Biswas, Y. Yıldırım, A. Alshomrani","doi":"10.37256/cm.5120244121","DOIUrl":"https://doi.org/10.37256/cm.5120244121","url":null,"abstract":"This paper introduces a state of the art investigation into the interaction between soliton propagation and differential group delay, offering a fresh perspective often neglected in previous studies. Motivated by the imperative to comprehend soliton behavior within inter-modal dispersion environments, it presents three innovative methodologies aimed at uncovering novel optical soliton solutions. Through the utilization of cutting-edge algorithms, these approaches unveil the emergence of solitons in hitherto unexplored contexts. The research makes significant strides through extensive numerical simulations, which not only validate theoretical conjectures but also offer practical insights. Furthermore, it delineates crucial parameter limitations essential for the existence of solitons, thus furnishing valuable guidance for future research endeavors and practical applications.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140244162","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}
Solar thermal systems utilize solar energy to generate heat, and the incorporation of nanoparticles such as Al2O3-Cu-Ni with a water base can elevate their efficiency. These nanofluids, composed of aluminum oxide, copper, and nickel nanoparticles dispersed in water, enhance heat absorption and transfer within the system. This improvement contributes to heightened overall performance and effectiveness of solar thermal systems. Cupronickel alloy helps in the process of desalination. Hence, this study examines the heat exchange properties in the context of a boundary layer flow of a trihybrid over a variable-thickness Riga plate stretched and heated by convective heat with non-Newtonian fluid (Jeffery) in the presence of thermal radiation. The governing equations of the boundary layer are transformed into a system of ordinary differential equations through appropriate similarity transformations, and those equations are resolved utilizing a boundary value problem program. The engineering parameters are analyzed through the application of multiple linear regression. The key finding of the investigation is that the Prandtl number, and thickness index number all have a positive impact on the Nusselt number. The presence of radiation and a uniform heat source improves the Nusselt number, physically this energy transfer improvement assists in higher solar collector efficacy; and converts that energy to usable heat. The rationale behind selecting trihybrid nanoparticles Al2O3, Cu, and Ni lies in the balance and inertness of Al2O3, with metals Cu, and Ni, both possessing more thermal conductivity.
太阳能热系统利用太阳能产生热量，在水基中加入 Al2O3-Cu-Ni 等纳米颗粒可提高其效率。这些纳米流体由分散在水中的氧化铝、铜和镍纳米颗粒组成，可增强系统内的热量吸收和传递。这种改进有助于提高太阳能热系统的整体性能和效率。铜镍合金有助于海水淡化过程。因此，本研究考察了在热辐射存在的情况下，三混合物在拉伸厚度可变的里加板上的边界层流动的热交换特性，以及非牛顿流体（杰弗里）的对流热量。通过适当的相似变换，边界层的支配方程被转换成常微分方程系统，并利用边界值问题程序解决这些方程。工程参数通过应用多元线性回归进行分析。研究的主要发现是，普朗特数和厚度指数都对努塞尔特数有积极影响。辐射和均匀热源的存在提高了努塞尔特数，从物理上讲，这种能量传递的改善有助于提高太阳能集热器的效率，并将能量转化为可用热量。选择 Al2O3、Cu 和 Ni 三种杂化纳米粒子的理由在于 Al2O3 与金属 Cu 和 Ni 之间的平衡和惰性，两者都具有更强的导热性。
{"title":"Radiative Impact on Jeffery Trihybrid Convective Nanoflow over an Extensible Riga Plate: Multiple Linear Regression Analysis","authors":"N. Bhargavi, Poornima T","doi":"10.37256/cm.5120244058","DOIUrl":"https://doi.org/10.37256/cm.5120244058","url":null,"abstract":"Solar thermal systems utilize solar energy to generate heat, and the incorporation of nanoparticles such as Al2O3-Cu-Ni with a water base can elevate their efficiency. These nanofluids, composed of aluminum oxide, copper, and nickel nanoparticles dispersed in water, enhance heat absorption and transfer within the system. This improvement contributes to heightened overall performance and effectiveness of solar thermal systems. Cupronickel alloy helps in the process of desalination. Hence, this study examines the heat exchange properties in the context of a boundary layer flow of a trihybrid over a variable-thickness Riga plate stretched and heated by convective heat with non-Newtonian fluid (Jeffery) in the presence of thermal radiation. The governing equations of the boundary layer are transformed into a system of ordinary differential equations through appropriate similarity transformations, and those equations are resolved utilizing a boundary value problem program. The engineering parameters are analyzed through the application of multiple linear regression. The key finding of the investigation is that the Prandtl number, and thickness index number all have a positive impact on the Nusselt number. The presence of radiation and a uniform heat source improves the Nusselt number, physically this energy transfer improvement assists in higher solar collector efficacy; and converts that energy to usable heat. The rationale behind selecting trihybrid nanoparticles Al2O3, Cu, and Ni lies in the balance and inertness of Al2O3, with metals Cu, and Ni, both possessing more thermal conductivity.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140242707","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}
In this research paper, an investigation of charge and current flow in an LCR series circuit has been presented. For this purpose, basis functions of Chebyshev wavelets of the second kind have been utilized. The proposed method involves representing the highest-order derivatives as a series of basis functions using Chebyshev wavelets. In order to demonstrate the effectiveness of this approach, numerical examples have been provided, and their results are presented to show the accuracy of the proposed scheme.
{"title":"Analysis of Charge and Current Flow in the LCR Series Circuit via Chebyshev Wavelets","authors":"Inderdeep Singh, Preeti","doi":"10.37256/cm.5120242822","DOIUrl":"https://doi.org/10.37256/cm.5120242822","url":null,"abstract":"In this research paper, an investigation of charge and current flow in an LCR series circuit has been presented. For this purpose, basis functions of Chebyshev wavelets of the second kind have been utilized. The proposed method involves representing the highest-order derivatives as a series of basis functions using Chebyshev wavelets. In order to demonstrate the effectiveness of this approach, numerical examples have been provided, and their results are presented to show the accuracy of the proposed scheme.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140245357","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}
Puneet Shrama, Ioannis K. Argyros, R. Behl, V. Kanwar
We propose and study a new Jungck-type iteration scheme to approximate coincidence points of contractive mappings. The strong convergence, stability, and data dependency results have been discussed. Numerical experiments demonstrate that the newly introduced Jungck-type iteration scheme yields a higher convergence rate in comparison with other Jungck-type iteration schemes available in the literature.
{"title":"Stability and Data Dependence Results for Jungck-type Iteration Scheme","authors":"Puneet Shrama, Ioannis K. Argyros, R. Behl, V. Kanwar","doi":"10.37256/cm.5120242525","DOIUrl":"https://doi.org/10.37256/cm.5120242525","url":null,"abstract":"We propose and study a new Jungck-type iteration scheme to approximate coincidence points of contractive mappings. The strong convergence, stability, and data dependency results have been discussed. Numerical experiments demonstrate that the newly introduced Jungck-type iteration scheme yields a higher convergence rate in comparison with other Jungck-type iteration schemes available in the literature.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140246971","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}
M. Ipopa, Brice Landry Doumbé Bangola, Armel Andami Ovono
This paper is concerned with the study of the asymptotic behavior of a generalization of the Caginalp phase-field model subject to homogeneous Neumann boundary conditions and regular potentials involving two temperatures. This work follows on from a paper in which the well-posedness of the problem, the dissipativity of the system, and the existence of global and exponential attractors were demonstrated. In addition, a study on the semi-infinite cylinder was also carried out. Indeed, if it is true that the existence of a global attractor makes it possible to predict the asymptotic behavior of solutions on a bounded domain, it does not say that these solutions converge. After having shown the existence of the global attractor, it is therefore important to look at the convergence of the solutions over time. There are several methods for determining the asymptotic behavior of the solutions of a differential system. We can mention the one that consists of transforming the given differential equations into integral equations and then applying the classical Picard successive approximation procedure to them. This work is devoted to the study of the convergence of solutions to steady states, adapting a well-known result concerning Lojasiewicz-Simon’s inequality.
{"title":"Stability of Solutions to a Caginalp Phase-Field Type Equations","authors":"M. Ipopa, Brice Landry Doumbé Bangola, Armel Andami Ovono","doi":"10.37256/cm.5120242725","DOIUrl":"https://doi.org/10.37256/cm.5120242725","url":null,"abstract":"This paper is concerned with the study of the asymptotic behavior of a generalization of the Caginalp phase-field model subject to homogeneous Neumann boundary conditions and regular potentials involving two temperatures. This work follows on from a paper in which the well-posedness of the problem, the dissipativity of the system, and the existence of global and exponential attractors were demonstrated. In addition, a study on the semi-infinite cylinder was also carried out. Indeed, if it is true that the existence of a global attractor makes it possible to predict the asymptotic behavior of solutions on a bounded domain, it does not say that these solutions converge. After having shown the existence of the global attractor, it is therefore important to look at the convergence of the solutions over time. There are several methods for determining the asymptotic behavior of the solutions of a differential system. We can mention the one that consists of transforming the given differential equations into integral equations and then applying the classical Picard successive approximation procedure to them. This work is devoted to the study of the convergence of solutions to steady states, adapting a well-known result concerning Lojasiewicz-Simon’s inequality.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140245737","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}
In this paper, the approximate boundary controllability of Hilfer fractional neutral stochastic differential inclusions with fractional Brownian motion (fBm) and Clarke’s subdifferential in Hilbert space is discussed. The existence of a mild solution of Hilfer fractional neutral stochastic differential inclusions with fractional Brownian motion and Clarke’s subdifferential is proved by using fractional calculus, compact semigroups, the fixed point theorem, stochastic analysis, and multivalued maps. The required conditions for the approximate boundary controllability of this system are defined according to a corresponding linear system that is approximately controllable. To demonstrate how our primary findings may be used, a final example is provided.
{"title":"Hilfer Fractional Neutral Stochastic Differential Inclusions with Clarke’s Subdifferential Type and fBm: Approximate Boundary Controllability","authors":"K. Nandhaprasadh, R. Udhayakumar","doi":"10.37256/cm.5120243580","DOIUrl":"https://doi.org/10.37256/cm.5120243580","url":null,"abstract":"In this paper, the approximate boundary controllability of Hilfer fractional neutral stochastic differential inclusions with fractional Brownian motion (fBm) and Clarke’s subdifferential in Hilbert space is discussed. The existence of a mild solution of Hilfer fractional neutral stochastic differential inclusions with fractional Brownian motion and Clarke’s subdifferential is proved by using fractional calculus, compact semigroups, the fixed point theorem, stochastic analysis, and multivalued maps. The required conditions for the approximate boundary controllability of this system are defined according to a corresponding linear system that is approximately controllable. To demonstrate how our primary findings may be used, a final example is provided.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140250220","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}
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