Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4864
H. R. Abdl-Rahim, Hijaz Ahmad, Taher A. Nofal, G. M. Ismail
This paper studies the epidemic model of rational order via an efficient genius modern analytical approximate technique named Natural Transform Adomian Decomposition Method (NTADM). It is based on Caputo fractional derivative. To demonstrate the effectiveness of the present method, the results are displayed in graphs. Accordingly, the NTADM can be very easily applied to other nonlinear models.
{"title":"Analytical and Approximate Solutions for Fractional Systems of Nonlinear Differential Equations","authors":"H. R. Abdl-Rahim, Hijaz Ahmad, Taher A. Nofal, G. M. Ismail","doi":"10.29020/nybg.ejpam.v16i4.4864","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4864","url":null,"abstract":"This paper studies the epidemic model of rational order via an efficient genius modern analytical approximate technique named Natural Transform Adomian Decomposition Method (NTADM). It is based on Caputo fractional derivative. To demonstrate the effectiveness of the present method, the results are displayed in graphs. Accordingly, the NTADM can be very easily applied to other nonlinear models.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"1983 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068829","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4947
Ahmed Salem Heilat
This paper introduces a novel trigonometric B-spline collocation method for solving a specific class of second-order boundary value problems. The study showcases the method’s practicality and effectiveness through various numerical examples. Furthermore, it evaluates the technique’s performance by calculating maximum errors for different step sizes in the spatial domain. The paper also conducts a comparative analysis with alternative methods, demonstrating the superior accuracy of the trigonometric B-spline approach.
{"title":"Cubic Trigonometric B-spline Method for Solving a Linear System of Second Order Boundary Value Problems","authors":"Ahmed Salem Heilat","doi":"10.29020/nybg.ejpam.v16i4.4947","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4947","url":null,"abstract":"This paper introduces a novel trigonometric B-spline collocation method for solving a specific class of second-order boundary value problems. The study showcases the method’s practicality and effectiveness through various numerical examples. Furthermore, it evaluates the technique’s performance by calculating maximum errors for different step sizes in the spatial domain. The paper also conducts a comparative analysis with alternative methods, demonstrating the superior accuracy of the trigonometric B-spline approach.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"33 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068830","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4888
Hassan Kanj, Hifza Iqbal, Muhammad Haroon Aftab, Hasnain Raza, Kamel Jebreen, Mohammed Issa Sowaity
Graph theory has great deal of application in disciplines like biology, computer science, informatics, engineering, mathematics, social science, linguistics and medicine. Topological indices are created by labeling the chemical structure through numerical parameters. These notations link chemical compounds physicochemical features such as boiling temperature, stability, strain energy etc, to its molecular structure. Different topological features of chemical structure have been explored. One of the molecular graphs topological indices are the connection indices defined on the number of connection between vertices of distance two. In this work, we compute the first Zagreb connection index, second Zagreb connection index, and modified first Zagreb connection index for hexagonal network and non kekulean benzenoid hydrocarbon.
{"title":"Topological Characterization of Hexagonal Network and Non-Kekulean Benzenoid Hydrocarbon","authors":"Hassan Kanj, Hifza Iqbal, Muhammad Haroon Aftab, Hasnain Raza, Kamel Jebreen, Mohammed Issa Sowaity","doi":"10.29020/nybg.ejpam.v16i4.4888","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4888","url":null,"abstract":"Graph theory has great deal of application in disciplines like biology, computer science, informatics, engineering, mathematics, social science, linguistics and medicine. Topological indices are created by labeling the chemical structure through numerical parameters. These notations link chemical compounds physicochemical features such as boiling temperature, stability, strain energy etc, to its molecular structure. Different topological features of chemical structure have been explored. One of the molecular graphs topological indices are the connection indices defined on the number of connection between vertices of distance two. In this work, we compute the first Zagreb connection index, second Zagreb connection index, and modified first Zagreb connection index for hexagonal network and non kekulean benzenoid hydrocarbon.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"16 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068837","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4862
Al-Amin Y. Isahac, Javier Hassan, Ladznar S. Laja, Hounam B. Copel
Let G be a graph with vertex and edge sets V (G) and E(G), respectively. A set C ⊆ V (G) is called an outer-convex hop dominating if for every two vertices x, y ∈ V (G) C, the vertex set of every x−y geodesic is contained in V (G) C and for every a ∈ V (G) C, there exists b ∈ C such that dG(a, b) = 2. The minimum cardinality of an outer-convex hop dominating set of G, denoted by ̃γconh(G), is called the outer-convex hop domination number of G. In this paper, we generate some formulas for the parameters of some special graphs and graphs under some binary operations by characterizing first the outer-convex hop dominating sets of each of thesegraphs. Moreover, we establish realization result that identifies and determines the connection of this parameter with the standard hop domination parameter. It shows that given any graph, this new parameter is always greater than or equal to the standard hop domination parameter.
{"title":"Outer-Convex Hop Domination in Graphs Under Some Binary Operations","authors":"Al-Amin Y. Isahac, Javier Hassan, Ladznar S. Laja, Hounam B. Copel","doi":"10.29020/nybg.ejpam.v16i4.4862","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4862","url":null,"abstract":"Let G be a graph with vertex and edge sets V (G) and E(G), respectively. A set C ⊆ V (G) is called an outer-convex hop dominating if for every two vertices x, y ∈ V (G) C, the vertex set of every x−y geodesic is contained in V (G) C and for every a ∈ V (G) C, there exists b ∈ C such that dG(a, b) = 2. The minimum cardinality of an outer-convex hop dominating set of G, denoted by ̃γconh(G), is called the outer-convex hop domination number of G. In this paper, we generate some formulas for the parameters of some special graphs and graphs under some binary operations by characterizing first the outer-convex hop dominating sets of each of thesegraphs. Moreover, we establish realization result that identifies and determines the connection of this parameter with the standard hop domination parameter. It shows that given any graph, this new parameter is always greater than or equal to the standard hop domination parameter.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069133","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4971
Meraa Arab
This paper focuses on the construction of traveling wave solutions to the nonlinear Klein--Gordon equation by employing the qualitative theory of planar dynamical systems. Based on this theory, we analytically study the existence of periodic, kink (anti-kink), and solitary wave solutions. We then attempt to construct such solutions. For this purpose, we apply a well-known traveling wave solution to convert the nonlinear Klein--Gordon equation into an ordinary differential equation that can be written as a one-dimensional Hamiltonian system. The qualitative theory is applied to investigate and describe phase portraits of the Hamiltonian system. Based on the bifurcation constraints on the system parameters, we integrate the conserved quantities to build new wave solutions that can be classified into periodic, kink (anti-kink), and solitary wave solutions. Some of the obtained solutions are clarified graphically and their connection with the phase orbits is derived.
{"title":"Bifurcation and Exact Traveling Wave Solutions for the Nonlinear Klein-Gordon Equation","authors":"Meraa Arab","doi":"10.29020/nybg.ejpam.v16i4.4971","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4971","url":null,"abstract":"This paper focuses on the construction of traveling wave solutions to the nonlinear Klein--Gordon equation by employing the qualitative theory of planar dynamical systems. Based on this theory, we analytically study the existence of periodic, kink (anti-kink), and solitary wave solutions. We then attempt to construct such solutions. For this purpose, we apply a well-known traveling wave solution to convert the nonlinear Klein--Gordon equation into an ordinary differential equation that can be written as a one-dimensional Hamiltonian system. The qualitative theory is applied to investigate and describe phase portraits of the Hamiltonian system. Based on the bifurcation constraints on the system parameters, we integrate the conserved quantities to build new wave solutions that can be classified into periodic, kink (anti-kink), and solitary wave solutions. Some of the obtained solutions are clarified graphically and their connection with the phase orbits is derived.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068838","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4958
Shoura Ahmed Balatta, Eddie Shahril Ismail, Ishak Hashim, Ahmad Sami Bataineh, Shaher Momani
The aim of this research is to study the oscillatory properties of higher -order delay half linear differential equations with non-canonical operators. Two methods for establishing some new conditions for the oscillation of all solutions of higher-order differential equations will be presented. The first method to use the Riccati transformations which differ from those reported in some literature. The second method employs comparison principles with first-order delay differential equations which can easily deduce oscillation of all solutions of studied equations. Not only do the newly proposed criteria improve, extend, and greatly simplify the previously established criteria, but they also have the potential to act as a reference point for the theory of delay differential equations of higher order, which is still in its early stages of development. We were able to determine three fundamental theorems regarding the oscillation of this equation. There will be some examples provided to illustrate the findings.
{"title":"Oscillatory Behavior of Higher-Order Differential Equations with Delay Terms","authors":"Shoura Ahmed Balatta, Eddie Shahril Ismail, Ishak Hashim, Ahmad Sami Bataineh, Shaher Momani","doi":"10.29020/nybg.ejpam.v16i4.4958","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4958","url":null,"abstract":"The aim of this research is to study the oscillatory properties of higher -order delay half linear differential equations with non-canonical operators. Two methods for establishing some new conditions for the oscillation of all solutions of higher-order differential equations will be presented. The first method to use the Riccati transformations which differ from those reported in some literature. The second method employs comparison principles with first-order delay differential equations which can easily deduce oscillation of all solutions of studied equations. Not only do the newly proposed criteria improve, extend, and greatly simplify the previously established criteria, but they also have the potential to act as a reference point for the theory of delay differential equations of higher order, which is still in its early stages of development. We were able to determine three fundamental theorems regarding the oscillation of this equation. There will be some examples provided to illustrate the findings.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"35 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068986","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4882
Pannawit Khamrot, Natthinee Deetae
This paper presents an expansion of the generalized extreme value distribution to new distribution classes, specifically the Alpha Power Transformation Generalized Extreme Value (APTGEV) distribution. This extension is achieved by combining the Extreme Value theory and the alpha power transformation technique. We employ the maximum likelihood method in conjunction with the Newton-Raphson procedure to estimate the parameters in these proposed distributions. In the final stages of our research, we simulate these new distributions and apply them to real-world data. For this study, we have chosen extreme rainfall data from a weather station in the Si Samrong District Sukhothai Province of Thailand as our dataset. These extended distribution classes are designed to provide greater flexibility and adaptability in understanding complex data patterns, and their application to real-world data offers valuable insights into their effectiveness.
{"title":"A New Class of Generalized Extreme Value Distribution and Application under Alpha Power Transformation Method","authors":"Pannawit Khamrot, Natthinee Deetae","doi":"10.29020/nybg.ejpam.v16i4.4882","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4882","url":null,"abstract":"This paper presents an expansion of the generalized extreme value distribution to new distribution classes, specifically the Alpha Power Transformation Generalized Extreme Value (APTGEV) distribution. This extension is achieved by combining the Extreme Value theory and the alpha power transformation technique. We employ the maximum likelihood method in conjunction with the Newton-Raphson procedure to estimate the parameters in these proposed distributions. In the final stages of our research, we simulate these new distributions and apply them to real-world data. For this study, we have chosen extreme rainfall data from a weather station in the Si Samrong District Sukhothai Province of Thailand as our dataset. These extended distribution classes are designed to provide greater flexibility and adaptability in understanding complex data patterns, and their application to real-world data offers valuable insights into their effectiveness.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"0 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068989","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4919
Abdelrahman Yousef, Roshdi Khalil, Abdullah Tallafha, B. Mutabagani
In an attempt to solve the farthest point problem, we introduce a new class of uniquely remotal sets. Namely, the class of uniquely distant sets. Then, we prove that in a separable Hilbert space, every uniquely distant set is a singleton.
{"title":"On The Farthest Point Problem In Hilbert Spaces","authors":"Abdelrahman Yousef, Roshdi Khalil, Abdullah Tallafha, B. Mutabagani","doi":"10.29020/nybg.ejpam.v16i4.4919","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4919","url":null,"abstract":"In an attempt to solve the farthest point problem, we introduce a new class of uniquely remotal sets. Namely, the class of uniquely distant sets. Then, we prove that in a separable Hilbert space, every uniquely distant set is a singleton.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"25 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068991","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4736
Chawalit Boonpok, Napassanan Srisarakham
This paper deals with the concept of generalized $delta p(Lambda,s)$-closed sets. Especially, some properties of generalized $delta p(Lambda,s)$-closed sets are discussed. Moreover, we apply the notion of generalized $delta p(Lambda,s)$-closed sets to present and study new classes of spaces called $delta p(Lambda,s)$-$T_frac{1}{2}$-spaces and $delta p(Lambda,s)$-normal spaces. Several properties and characterizations concerning $delta p(Lambda,s)$-$T_frac{1}{2}$-spaces and $delta p(Lambda,s)$-normal spaces are established.
{"title":"Properties of Generalized $delta p(Lambda,s)$-closed Sets","authors":"Chawalit Boonpok, Napassanan Srisarakham","doi":"10.29020/nybg.ejpam.v16i4.4736","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4736","url":null,"abstract":"This paper deals with the concept of generalized $delta p(Lambda,s)$-closed sets. Especially, some properties of generalized $delta p(Lambda,s)$-closed sets are discussed. Moreover, we apply the notion of generalized $delta p(Lambda,s)$-closed sets to present and study new classes of spaces called $delta p(Lambda,s)$-$T_frac{1}{2}$-spaces and $delta p(Lambda,s)$-normal spaces. Several properties and characterizations concerning $delta p(Lambda,s)$-$T_frac{1}{2}$-spaces and $delta p(Lambda,s)$-normal spaces are established.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"25 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068993","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4868
Harren Campos, Jezer Fernandez, Jade Bong Natuil
This paper is motivated by the work of Taekyun Kim and Dae San Kim on the degenerate Laplace transform and degenerate gamma function, as published in the Russian Journal of Mathematical Physics. We introduce the degenerate Laplace-type integral transform and delve into its properties and interrelations. This paper focuses on the degenerate Laplace-type integral transforms of several fundamental functions, including the degenerate sine, degenerate cosine, degenerate hyperbolic sine, and degenerate hyperbolic cosine functions. Furthermore, we establish crucial connections between the degenerate Laplace-type integral transform and existing degenerate integral transforms. Specifically, we explore its relationships with the degenerate Laplace transform, the degenerate Elzaki transform, and the degenerate Sumudu transforms.
这篇论文的灵感来自于Taekyun Kim和Dae San Kim关于简并拉普拉斯变换和简并伽马函数的研究，该研究发表在《俄罗斯数学物理杂志》上。引入简并拉普拉斯型积分变换，探讨其性质和相互关系。本文研究了退化正弦、退化余弦、退化双曲正弦、退化双曲余弦等基本函数的退化拉普拉斯型积分变换。进一步建立了退化拉普拉斯型积分变换与现有退化拉普拉斯型积分变换之间的重要联系。具体来说，我们探讨了它与简并拉普拉斯变换、简并Elzaki变换和简并Sumudu变换的关系。
{"title":"On Degenerate Laplace-type Integral Transform","authors":"Harren Campos, Jezer Fernandez, Jade Bong Natuil","doi":"10.29020/nybg.ejpam.v16i4.4868","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4868","url":null,"abstract":"This paper is motivated by the work of Taekyun Kim and Dae San Kim on the degenerate Laplace transform and degenerate gamma function, as published in the Russian Journal of Mathematical Physics. We introduce the degenerate Laplace-type integral transform and delve into its properties and interrelations. This paper focuses on the degenerate Laplace-type integral transforms of several fundamental functions, including the degenerate sine, degenerate cosine, degenerate hyperbolic sine, and degenerate hyperbolic cosine functions. Furthermore, we establish crucial connections between the degenerate Laplace-type integral transform and existing degenerate integral transforms. Specifically, we explore its relationships with the degenerate Laplace transform, the degenerate Elzaki transform, and the degenerate Sumudu transforms.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"205 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069305","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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