Pub Date : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5043
K. Boulehmi
This study aims to use a novel scheme for the Atangana-Baleanu Caputo fractional derivative (ABC-FD) to solve the fractional Bernoulli equation and the fractional R ̈ossler model. Furthermore, the suggested technique is compared to Runge-Kutta Fourth Order (RK4). The proposed method is efficacious and generates solutions that are indistinguishable from the approx-imate solutions generated by the RK4 method. Therefore, we can adapt the approach to various systems and develop results that are more accurate. On top of that, the new technique (ABC-FD) can identify chaotic situations. Consequently, this approach can be used to enhance the performance of other systems. In the future, this technique can be employed to determine the numerical solution for a multitude of models applicable in the fields of science and engineering.
本研究旨在使用一种新颖的阿坦加纳-巴莱亚努-卡普托分数导数（ABC-FD）方案来求解分数伯努利方程和分数 R ̈ossler 模型。此外，还将所建议的技术与 Runge-Kutta 四阶 (RK4) 进行了比较。建议的方法是有效的，其生成的解与 RK4 方法生成的近似解没有区别。因此，我们可以将该方法应用于各种系统，并开发出更精确的结果。此外，新技术（ABC-FD）还能识别混沌情况。因此，这种方法可用于提高其他系统的性能。未来，这种技术可用于确定适用于科学和工程领域的多种模型的数值解。
{"title":"A Novel Numerical Scheme for Fractional Bernoulli Equations and the Rössler Model: A Comparative Analysis using Atangana-Baleanu Caputo Fractional Derivative","authors":"K. Boulehmi","doi":"10.29020/nybg.ejpam.v17i1.5043","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5043","url":null,"abstract":"This study aims to use a novel scheme for the Atangana-Baleanu Caputo fractional derivative (ABC-FD) to solve the fractional Bernoulli equation and the fractional R ̈ossler model. Furthermore, the suggested technique is compared to Runge-Kutta Fourth Order (RK4). The proposed method is efficacious and generates solutions that are indistinguishable from the approx-imate solutions generated by the RK4 method. Therefore, we can adapt the approach to various systems and develop results that are more accurate. On top of that, the new technique (ABC-FD) can identify chaotic situations. Consequently, this approach can be used to enhance the performance of other systems. In the future, this technique can be employed to determine the numerical solution for a multitude of models applicable in the fields of science and engineering.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140479725","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4798
Sandeep Kumar, Deepa Sinha
An ordered pair $Sigma = (Sigma^{u}$,$sigma$) is called the textit{signed graph}, where $Sigma^{u} = (V,E)$ is a textit{underlying graph} and $sigma$ is a signed mapping, called textit{signature}, from $E$ to the sign set $lbrace +, - rbrace$. The textit{splitting signed graph} $Gamma(Sigma)$ of a signed graph $Sigma$ is defined as, for every vertex $u in V(Sigma)$, take a new vertex $u'$. Join $u'$ to all the vertices of $Sigma$ adjacent to $u$ such that $sigma_{Gamma}(u'v) = sigma(u'v), u in N(v)$. The objective of this paper is to propose an algorithm for the generation of a splitting signed graph, a splitting root signed graph from a given signed graph using Matlab. Additionally, we conduct a spectral analysis of the resulting graph. Spectral analysis is performed on the adjacency and laplacian matrices of the splitting signed graph to study its eigenvalues and eigenvectors. A relationship between the energy of the original signed graph $Sigma$ and the energy of the splitting signed graph $Gamma(Sigma)$ is established.
{"title":"Spectral Analysis of Splitting Signed Graph","authors":"Sandeep Kumar, Deepa Sinha","doi":"10.29020/nybg.ejpam.v17i1.4798","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4798","url":null,"abstract":"An ordered pair $Sigma = (Sigma^{u}$,$sigma$) is called the textit{signed graph}, where $Sigma^{u} = (V,E)$ is a textit{underlying graph} and $sigma$ is a signed mapping, called textit{signature}, from $E$ to the sign set $lbrace +, - rbrace$. The textit{splitting signed graph} $Gamma(Sigma)$ of a signed graph $Sigma$ is defined as, for every vertex $u in V(Sigma)$, take a new vertex $u'$. Join $u'$ to all the vertices of $Sigma$ adjacent to $u$ such that $sigma_{Gamma}(u'v) = sigma(u'v), u in N(v)$. The objective of this paper is to propose an algorithm for the generation of a splitting signed graph, a splitting root signed graph from a given signed graph using Matlab. Additionally, we conduct a spectral analysis of the resulting graph. Spectral analysis is performed on the adjacency and laplacian matrices of the splitting signed graph to study its eigenvalues and eigenvectors. A relationship between the energy of the original signed graph $Sigma$ and the energy of the splitting signed graph $Gamma(Sigma)$ is established.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140471647","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4803
Badr Alharbi
Let F be a transversally oriented codimension-one foliation of class Cr, r ≥ 0, on a closed manifold M. A leaf class of a leaf F is the union of all leaves having the same closure as F . Let X be the leaf classes space and X0 be the union of all open subsets of X homeomorphic to R or S1. In [2, Theorem 3.15] it is shown that if a codimension one foliation has a finite height, then the singular part of the space of leaf classes is homeomorphic to the prime spectrum (or simply the spectrum) of unitary commutative ring. In this paper we prove that the singular part of the space of leaf classes is homeomorphic to the spectrum of unitary commutative ring if and only if every family of totaly ordered leaves is bounded below.
让 F 是闭合流形 M 上类 Cr 的横向定向一维叶片，r ≥ 0。叶片 F 的叶类是与 F 具有相同闭合的所有叶片的联合。设 X 是叶类空间，X0 是 X 的所有同构于 R 或 S1 的开放子集的联合。在[2，定理 3.15]中证明，如果一个标度为一的叶子具有有限高，那么叶类空间的奇异部分与单元换元环的素谱（或简称谱）同构。在本文中，我们将证明当且仅当每一个全有序叶族都在下面有界时，叶类空间的奇异部分与单元交换环的谱是同构的。
{"title":"Codimension One Foliation and the Prime Spectrum of a Ring","authors":"Badr Alharbi","doi":"10.29020/nybg.ejpam.v17i1.4803","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4803","url":null,"abstract":"Let F be a transversally oriented codimension-one foliation of class Cr, r ≥ 0, on a closed manifold M. A leaf class of a leaf F is the union of all leaves having the same closure as F . Let X be the leaf classes space and X0 be the union of all open subsets of X homeomorphic to R or S1. In [2, Theorem 3.15] it is shown that if a codimension one foliation has a finite height, then the singular part of the space of leaf classes is homeomorphic to the prime spectrum (or simply the spectrum) of unitary commutative ring. In this paper we prove that the singular part of the space of leaf classes is homeomorphic to the spectrum of unitary commutative ring if and only if every family of totaly ordered leaves is bounded below.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140471993","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4735
C. Boonpok, P. Pue-on
Our main purpose is to introduce the concept of $delta p(Lambda,s)$-$R_0$ spaces. Moreover, somecharacterizations of $delta p(Lambda,s)$-$R_0$ spaces are investigated.
{"title":"Characterizations of $delta p(Lambda,s)$-$R_0$ Spaces","authors":"C. Boonpok, P. Pue-on","doi":"10.29020/nybg.ejpam.v17i1.4735","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4735","url":null,"abstract":"Our main purpose is to introduce the concept of $delta p(Lambda,s)$-$R_0$ spaces. Moreover, somecharacterizations of $delta p(Lambda,s)$-$R_0$ spaces are investigated.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140479133","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4823
Q. H. Khan, Sameh Askar, Shahbaz Ali, Hijaz Ahmad
In this paper, we prove the results on existence and uniqueness of fixed points in the setting of symmetric space under ψ-contractions using a binary relation. We also provide some examples to illustrate our newly proved results.
{"title":"Fixed Point Theorem in Symmetric Space Employing (c)- comparison Functions and Binary relation","authors":"Q. H. Khan, Sameh Askar, Shahbaz Ali, Hijaz Ahmad","doi":"10.29020/nybg.ejpam.v17i1.4823","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4823","url":null,"abstract":"In this paper, we prove the results on existence and uniqueness of fixed points in the setting of symmetric space under ψ-contractions using a binary relation. We also provide some examples to illustrate our newly proved results.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140478762","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5003
Lyster Rey Cabardo, Gaudencio C. Petalcorin, Jr.
A hyper $BN$-algebra is a nonempty set $H$ together with a hyperoperation ``$circledast$'' and a constant $0$ such that for all $x, y, z in H$: $x ll x$, $x circledast 0 = {x}$, and $(x circledast y) circledast z = (0 circledast z) circledast (y circledast x)$, where $x ll y$ if and only if $0 in x circledast y$. We investigated the structures of ideals in the Hyper $BN$-algebra setting. We established equivalency of weak hyper $BN$-ideals and hyper sub$BN$-algebras. Also, we found a condition when a strong hyper $BN$-ideal become a hyper $BN$-ideal. Finally, we looked at two ways in constructing the quotient hyper $BN$-algebras and investigated the relationship between the two constructions.
{"title":"Looking at Two Ways of Constructing Quotient Hyper $BN$-algebras and Some Notes on Hyper $BN$-ideals","authors":"Lyster Rey Cabardo, Gaudencio C. Petalcorin, Jr.","doi":"10.29020/nybg.ejpam.v17i1.5003","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5003","url":null,"abstract":"A hyper $BN$-algebra is a nonempty set $H$ together with a hyperoperation ``$circledast$'' and a constant $0$ such that for all $x, y, z in H$: $x ll x$, $x circledast 0 = {x}$, and $(x circledast y) circledast z = (0 circledast z) circledast (y circledast x)$, where $x ll y$ if and only if $0 in x circledast y$. We investigated the structures of ideals in the Hyper $BN$-algebra setting. We established equivalency of weak hyper $BN$-ideals and hyper sub$BN$-algebras. Also, we found a condition when a strong hyper $BN$-ideal become a hyper $BN$-ideal. Finally, we looked at two ways in constructing the quotient hyper $BN$-algebras and investigated the relationship between the two constructions.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140474638","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4858
C. Boonpok, Jeeranunt Khampakdee
Our main purpose is to introduce the concepts of upper and lower α-⋆-continuous multifunctions. In particular, some characterizations of upper and lower α-⋆-continuous multifunctions are investigated.
{"title":"Upper and Lower $alpha$-$star$-continuity","authors":"C. Boonpok, Jeeranunt Khampakdee","doi":"10.29020/nybg.ejpam.v17i1.4858","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4858","url":null,"abstract":"Our main purpose is to introduce the concepts of upper and lower α-⋆-continuous multifunctions. In particular, some characterizations of upper and lower α-⋆-continuous multifunctions are investigated.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140476720","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5022
Waleed AlRawashdeh
In this paper, we introduce and investigate a family of analytic functions, denoted by $mathcal{F}(Pi, alpha, beta, lambda, delta, mu)$, defined by means of Horadam polynomials. For functions in this family, we derive the estimations for the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$. Moreover, we obtain the classical Fekete-Szeg"{o} inequality of functions belonging to this family.
{"title":"A family of Analytic Functions Subordinate to Horadam Polynomials","authors":"Waleed AlRawashdeh","doi":"10.29020/nybg.ejpam.v17i1.5022","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5022","url":null,"abstract":"In this paper, we introduce and investigate a family of analytic functions, denoted by $mathcal{F}(Pi, alpha, beta, lambda, delta, mu)$, defined by means of Horadam polynomials. For functions in this family, we derive the estimations for the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$. Moreover, we obtain the classical Fekete-Szeg\"{o} inequality of functions belonging to this family.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140477618","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4975
C. Boonpok, Jeeranunt Khampakdee
Our main purpose is to introduce the concept of almost strongly θ(Λ, p)-continuous functions. Moreover, some characterizations of almost strongly θ(Λ, p)-continuous functions are considered.
{"title":"Almost strong $theta(Lambda,p)$-continuity for Functions","authors":"C. Boonpok, Jeeranunt Khampakdee","doi":"10.29020/nybg.ejpam.v17i1.4975","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4975","url":null,"abstract":"Our main purpose is to introduce the concept of almost strongly θ(Λ, p)-continuous functions. Moreover, some characterizations of almost strongly θ(Λ, p)-continuous functions are considered.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140473758","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5049
Khaled Saad, Mustafa Khirallah
In this paper, a numerical method for solving the fractional order Fredholm integro-differential equations via the Caputo-Liouville derivative is presented. The method uses the well-known shifted Chebyshev expansion and a truncated series to represent the unknown function. It also incorporates numerical integration techniques like the Trapezoidal, Simpson’s 1/3, and Simpson’s 8/3 methods. The paper also provides an approximation for the derivative of an integer. The procedure converts the provided problem into a system of algebraic equations using shifted Chebyshev coefficients and collocation points. The coefficients are found by solving this system using well-known techniques like Newton’s method. Numerical results are presented graphycally to illustrate the applicability, efficacy, and accuracy of the approach presented in this work. All calculations in this study were performed using the MATHEMATICA software program.
{"title":"A Spectral Collocation Method for Solving Caputo-Liouville Fractional Order Fredholm Integro-differential Equations","authors":"Khaled Saad, Mustafa Khirallah","doi":"10.29020/nybg.ejpam.v17i1.5049","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5049","url":null,"abstract":"In this paper, a numerical method for solving the fractional order Fredholm integro-differential equations via the Caputo-Liouville derivative is presented. The method uses the well-known shifted Chebyshev expansion and a truncated series to represent the unknown function. It also incorporates numerical integration techniques like the Trapezoidal, Simpson’s 1/3, and Simpson’s 8/3 methods. The paper also provides an approximation for the derivative of an integer. The procedure converts the provided problem into a system of algebraic equations using shifted Chebyshev coefficients and collocation points. The coefficients are found by solving this system using well-known techniques like Newton’s method. Numerical results are presented graphycally to illustrate the applicability, efficacy, and accuracy of the approach presented in this work. All calculations in this study were performed using the MATHEMATICA software program.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140472774","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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