Pub Date : 2023-11-30DOI: 10.5556/j.tkjm.55.2024.5158
Medjahed Djilali, Khellaf Ould Melha, V. L. Chinchane
In this paper, the extended Jacobi elliptic function expansion method is applied to conformable time-fractional Sasa-Satsumaequation. Variety of new traveling wave solutions are constructed. Thanks to the Mathematica software package, to interprete the behavior of some particular exact solutions, surfaces and contour plots are plotted.
{"title":"Various new traveling wave solutions for conformable time-fractional Sasa-Satsuma equation","authors":"Medjahed Djilali, Khellaf Ould Melha, V. L. Chinchane","doi":"10.5556/j.tkjm.55.2024.5158","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5158","url":null,"abstract":"In this paper, the extended Jacobi elliptic function expansion method is applied to conformable time-fractional Sasa-Satsumaequation. Variety of new traveling wave solutions are constructed. Thanks to the Mathematica software package, to interprete the behavior of some particular exact solutions, surfaces and contour plots are plotted.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"30 23","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139205605","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}
Pub Date : 2023-11-14DOI: 10.5556/j.tkjm.55.2024.5172
Pradeep Kumar, Anju Panwar
In this paper, a common solution of fixed point and generalized equilibrium problems using an asymptotically nonexpansive mapping is determined via iterative approach. Further, an application and numerical example of the main result are given.
{"title":"Common solutions of fixed point and generalized equilibrium problems using asymptotically nonexpansive mapping","authors":"Pradeep Kumar, Anju Panwar","doi":"10.5556/j.tkjm.55.2024.5172","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5172","url":null,"abstract":"In this paper, a common solution of fixed point and generalized equilibrium problems using an asymptotically nonexpansive mapping is determined via iterative approach. Further, an application and numerical example of the main result are given.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"84 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134901559","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 present work, we developed a deterministic SHATR (Susceptible - HIV infected -AIDS infected - Antiretroviral Treatment - Recovered) compartment model for HIV/AIDS. This model considers the disease outbreak due to a lack of awareness and treatment. The steady states of the proposed model system are obtained and analyzed by using the nonlinear stability theory of differential equations. The basic reproduction number is derived and explored to determine the stability and sensitivity index of some important relative parameters. Further, to know the global behavior of the model one parameter bifurcation study is discussed. Moreover, the optimal control theory has been applied to identify the optimal strategy by taking treatment and awareness for safe intercourse as control parameters. The control problem is solved analytically by using Pontryagin’s maximum principle. Finally, the model is simulated to describe the optimality under various assumptions and the stability of equilibrium points.
{"title":"Mathematical modeling and optimal control of a deterministic SHATR model of HIV/AIDS with possibility of rehabilitation: a dynamic analysis","authors":"Pankaj Singh Rana, Nitin Sharma, Anupam Priyadarshi","doi":"10.5556/j.tkjm.55.2024.5109","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5109","url":null,"abstract":"In the present work, we developed a deterministic SHATR (Susceptible - HIV infected -AIDS infected - Antiretroviral Treatment - Recovered) compartment model for HIV/AIDS. This model considers the disease outbreak due to a lack of awareness and treatment. The steady states of the proposed model system are obtained and analyzed by using the nonlinear stability theory of differential equations. The basic reproduction number is derived and explored to determine the stability and sensitivity index of some important relative parameters. Further, to know the global behavior of the model one parameter bifurcation study is discussed. Moreover, the optimal control theory has been applied to identify the optimal strategy by taking treatment and awareness for safe intercourse as control parameters. The control problem is solved analytically by using Pontryagin’s maximum principle. Finally, the model is simulated to describe the optimality under various assumptions and the stability of equilibrium points.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135469938","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 article, we demonstrate some fixed point results that generalises the Banachcontraction principle in a different way from the previously established literature findings. Weprovide some fixed point findings for non linear F type contractions in Strong Partial b-MetricSpaces (SPbMS). We also include some examples that demonstrates the applicability of ourfindings.
{"title":"Some fixed point results for nonlinear $F$-type contractions in strong partial b-metric spaces","authors":"None Savita Rathee, None Neelam Kumari, Monika Swami","doi":"10.5556/j.tkjm.55.2024.5145","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5145","url":null,"abstract":"In this article, we demonstrate some fixed point results that generalises the Banachcontraction principle in a different way from the previously established literature findings. Weprovide some fixed point findings for non linear F type contractions in Strong Partial b-MetricSpaces (SPbMS). We also include some examples that demonstrates the applicability of ourfindings.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135686330","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}
Pub Date : 2023-08-30DOI: 10.5556/j.tkjm.55.2024.5118
Bang-Yen Chen, Shihshu Walter Wei
By studying cohomology classes that are related with n-harmonic morphisms and F-harmonic maps, we augment and extend several results on F-harmonic maps, harmonic maps in [1, 3, 14], p-harmonic morphisms in [17], and also revisit our previous results in [9, 10, 21] on Riemannian submersions and n-harmonic morphisms which are submersions. The results, for example Theorem 3.2 obtaine by utilizing the n-conservation law (2.6), are sharp.
{"title":"$n$-harmonicity, minimality, conformality and cohomology","authors":"Bang-Yen Chen, Shihshu Walter Wei","doi":"10.5556/j.tkjm.55.2024.5118","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5118","url":null,"abstract":"
 
 
 By studying cohomology classes that are related with n-harmonic morphisms and F-harmonic maps, we augment and extend several results on F-harmonic maps, harmonic maps in [1, 3, 14], p-harmonic morphisms in [17], and also revisit our previous results in [9, 10, 21] on Riemannian submersions and n-harmonic morphisms which are submersions. The results, for example Theorem 3.2 obtaine by utilizing the n-conservation law (2.6), are sharp.
 
 
","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136162288","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}
Pub Date : 2023-08-25DOI: 10.5556/j.tkjm.55.2024.5127
Abel Nguelemo Kenfack, Francis Etienne Djiofack, David Dongo, Remy Magloire Etoua
We study the Einstein-Yang-Mills-Higgs (EYMH) system with a positive cosmological constant in the Bianchi type I space-time with locally rotational symmetry (LRS). In particular, we consider the nonlinear interaction of the Higgs field with the Yang-Mills field coupled to an unknown gravitational field. For the considered model, from certain additional conditions (the temporal gauge and some symmetries), we derive the conservation laws for the field equations and we then deduce the exact formulation of equations in the geometric framework. Furthermore, using an iterative approch and some mathematical analysis tools, we study the above system of equations. We then establish a global existence result for the homogeneous solution and we analyse its asymptotic behaviour.
{"title":"Asymptotic behaviour of the Einstein-Yang-Mills-Higgs system in a Bianchi type I model","authors":"Abel Nguelemo Kenfack, Francis Etienne Djiofack, David Dongo, Remy Magloire Etoua","doi":"10.5556/j.tkjm.55.2024.5127","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5127","url":null,"abstract":"We study the Einstein-Yang-Mills-Higgs (EYMH) system with a positive cosmological constant in the Bianchi type I space-time with locally rotational symmetry (LRS). In particular, we consider the nonlinear interaction of the Higgs field with the Yang-Mills field coupled to an unknown gravitational field. For the considered model, from certain additional conditions (the temporal gauge and some symmetries), we derive the conservation laws for the field equations and we then deduce the exact formulation of equations in the geometric framework. Furthermore, using an iterative approch and some mathematical analysis tools, we study the above system of equations. We then establish a global existence result for the homogeneous solution and we analyse its asymptotic behaviour.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134930675","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}
Pub Date : 2023-07-07DOI: 10.5556/j.tkjm.55.2024.5134
Arezoo Solimaninia, G. Afrouzi, H. Haghshenas
Based on the variational methods and critical-point theory, we are concerned with the existence results for a second-order impulsive boundary value problem involving an ordinary differential equation with $p(x)$-Laplacian operator, and Neumann conditions.
{"title":"Variational approach to impulsive Neumann problems with variable exponents and two parameters","authors":"Arezoo Solimaninia, G. Afrouzi, H. Haghshenas","doi":"10.5556/j.tkjm.55.2024.5134","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5134","url":null,"abstract":"Based on the variational methods and critical-point theory, we are concerned with the existence results for a second-order impulsive boundary value problem involving an ordinary differential equation with $p(x)$-Laplacian operator, and Neumann conditions.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"46 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80008295","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}
Pub Date : 2023-07-05DOI: 10.5556/j.tkjm.55.2023.5094
Mehdi Naimi, M. Benharrat
The main purpose of this paper is to give an improvement of numerical radius inequality for an upper triangular operator matrix.
本文的主要目的是给出上三角算子矩阵的数值半径不等式的一种改进。
{"title":"On the numerical radius of an upper triangular operator matrix","authors":"Mehdi Naimi, M. Benharrat","doi":"10.5556/j.tkjm.55.2023.5094","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2023.5094","url":null,"abstract":"The main purpose of this paper is to give an improvement of numerical radius inequality for an upper triangular operator matrix.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"2 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75858976","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}
Pub Date : 2023-05-22DOI: 10.5556/j.tkjm.55.2024.5126
Alex M. Montes, Ricardo Córdoba
Using an appropriate Carleman-type estimate, we establish a result of unique continuation for a special class of one-dimensional systems that model the evolution of long water waves with small amplitude in the presence of surface tension.
{"title":"A unique continuation result for a system of nonlinear differential equations","authors":"Alex M. Montes, Ricardo Córdoba","doi":"10.5556/j.tkjm.55.2024.5126","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5126","url":null,"abstract":"Using an appropriate Carleman-type estimate, we establish a result of unique continuation for a special class of one-dimensional systems that model the evolution of long water waves with small amplitude in the presence of surface tension.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"92 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83596170","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}
Pub Date : 2023-05-17DOI: 10.5556/j.tkjm.55.2024.5044
A. Siddiqui, K. Ahmad
In the sixties, A. Gray cite{Gr} and B. O'Neill cite{O1} come with the notion of Riemannian submersions as a tool to study the geometry of a Riemannian manifold with an additional structure in terms of the fibers and the base space. Riemannian submersions have long been an effective tool to construct Riemannian manifolds with positive or nonnegative sectional curvature in Riemannian geometry and compare certain manifolds within differential geometry. In particular, many examples of Einstein manifolds can be constructed by using such submersions. It is very well known that Riemannian submersions have applications in physics, for example Kaluza-Klein theory, Yang-Mills theory, supergravity and superstring theories.
{"title":"A study of statistical submersions","authors":"A. Siddiqui, K. Ahmad","doi":"10.5556/j.tkjm.55.2024.5044","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5044","url":null,"abstract":"In the sixties, A. Gray cite{Gr} and B. O'Neill cite{O1} come with the notion of Riemannian submersions as a tool to study the geometry of a Riemannian manifold with an additional structure in terms of the fibers and the base space. Riemannian submersions have long been an effective tool to construct Riemannian manifolds with positive or nonnegative sectional curvature in Riemannian geometry and compare certain manifolds within differential geometry. In particular, many examples of Einstein manifolds can be constructed by using such submersions. It is very well known that Riemannian submersions have applications in physics, for example Kaluza-Klein theory, Yang-Mills theory, supergravity and superstring theories.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76255002","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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