European Journal of Pure and Applied Mathematics https://jalgstat.com/index.php/ejpam <h3>Welcome</h3> <p align="justify">&nbsp;</p> <p align="justify"><em>European Journal of Pure and Applied Mathematics</em> is an Open Access international, peer-reviewed electronic journal which is devoted to high-quality and original research in the fields of pure and applied mathematics and their teaching and learning. The aim of the journal is to provide a medium by which a wide range of experience can be exchanged among researchers from diverse fields such as engineering, natural sciences or social sciences. This journal publishes high quality researches in the fields of contemporary pure and applied mathematics with a broad range of topics including algebra, topology, number theory, nonlinear analysis, mathematical methods in operations research, theoretical statistics and econometrics, and theoretical computer science.</p> <p align="justify">Open Access&nbsp;which is a paradigm shift in scholarly publishing means you can publish your research so it is free to access online as soon as it is published, that is, anyone can read (and circulate) freely and cite your work. Many funding agencies mandate publishing your research open access.</p> <p align="justify"><em>Editorial Board</em></p> <p align="justify">The<strong>&nbsp;</strong>Editorial Board consists of prominent scientists as some are&nbsp;Nobel Laureates.</p> <p align="justify">See&nbsp;<a href="/index.php/ejpam/about/editorialTeam">editorial board</a>&nbsp;details.</p> <p><em>Journal Impact</em><strong>&nbsp;</strong></p> <ul style="list-style-type: square;"> <li class="MsoNormal">Clarivate Analytics Web of Science Citation Report: Average citation per paper (impact factor): 0.61 between 2015 and 2018 from Web of Science Core Collection. This report reflects citations to source papers indexed within Web of Science Core Collection- retrieved on May 29, 2019.&nbsp;&nbsp;</li> <li class="MsoNormal">Clarivate Analytics Web of Science Citation Report: Average citation per paper (impact factor): 4.13 between 2008 and 2018 from Web of Science Core Collection. This report also includes citations to papers published before 2015, the starting year for the inclusion of EJPAM in Clarivate Analytics, within Web of Science Core Collection- retrieved on May 29, 2019.</li> <li class="MsoNormal">Harzing's Publish or Perish software:&nbsp;Cites/paper (impact factor): 5.41 and h-index: 24 between 2008 and 2018 from Google Scholar- retrieved on May 29, 2019.&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</li> </ul> <p><em>Abstracted/Indexed in:</em></p> <p align="justify">Clarivate Analytics Emerging Sources Citation Index (ESCI), Web of Science, <a title="EJPAM Scopus Source Details Page" href="https://www.scopus.com/sourceid/21100981084" target="_blank" rel="noopener">SCOPUS</a>, Mathematical Reviews, EBSCO, Chambridge Scientific Abstracts, IndexCopernicus&trade;, International Abstracts in Operations Research, Ulrich's Periodicals Directory, <a title="Arastirmax Bilimsel Yayın İndeksi" href="http://www.arastirmax.com/dergi/european-journal-pure-and-applied-mathematics" target="_blank" rel="noopener">Arastirmax</a>.</p> <p align="justify"><em>Publisher</em></p> <p align="justify">European Journal of Pure and Applied Mathematics is published by <em>New York Business Global, USA</em>.</p> <p align="justify"><em><em><span class="gmail_default">​</span></em></em><em>Prestigious Contributors</em></p> <div> <div><span class="gmail_default">In addition to Nobel Laureates and Abel Prize&nbsp;</span>Laureates<span class="gmail_default">, m</span>any researchers, authors and Editorial Board members<span class="gmail_default">&nbsp;at academic institutions such as University of Oxford, Harvard University, MIT, Stanford University, Princeton University, University of Chicago, Imperial College London and Berkeley,&nbsp;</span>and&nbsp;<span class="gmail_default">other institutions &nbsp;</span>have<span class="gmail_default">&nbsp;been</span>&nbsp;contribut<span class="gmail_default">ing</span>&nbsp;to EJPAM<span class="gmail_default">. Join them by submitting a paper.</span></div> </div> <div>&nbsp;&nbsp;</div> <div><em>Funding<span class="gmail_default">​/Granting​</span>&nbsp;Institutions</em></div> <div><em>&nbsp;</em></div> <div>Over the course of journal history, a majority of papers published at EJPAM have been financially supported by numerious leading universities and funding agencies all over the world including from University of Oxford, Danish National Research Foundation and&nbsp;Research Council of Norway&nbsp; to Robertson Foundation and King Abdulaziz&nbsp;<span class="gmail_default">​City for Science and Technology</span>, to National Natural Science Foundation of China and European Commission.</div> <div>&nbsp;</div> <div>ISSN:1307-5543 <br />Published by New York Business Global, Maryland, USA<br />Inaugural publication: January 2008 <br />The journal is quarterly</div> NNew York Business Global en-US European Journal of Pure and Applied Mathematics 1307-5543 <p align="justify">Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to <em>European Journal of Pure and Applied Mathematics. </em></p><p align="justify"><em>European Journal of Pure and Applied Mathematics will be Copyrihgt Holder.</em></p><p align="justify">If necessary, authors are responsible for obtaining permissions to reprint previously published figures, tables, and other material.</p> The Double Laplace Transform Expressed in terms of the Lerch Transcendent https://jalgstat.com/index.php/ejpam/article/view/3987 In this manuscript, the authors derive a formula for the double Laplace transform expressed in terms of the Lerch Transcendent. The log term mixes the variables so that the integral is not separable except for special values of k. The method of proof follows the method used by us to evaluate single integrals. This transform is then used to derive definite integrals in terms of fundamental constants, elementary and special functions. A summary of the results is produced in the form of a table of definite integrals for easy referencing by readers. Robert Reynolds Allan Stauffer Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 618 637 10.29020/nybg.ejpam.v14i3.3987 Stable Locating-Dominating Sets in Graphs https://jalgstat.com/index.php/ejpam/article/view/3998 A set S ⊆ V(G) of a (simple) undirected graph G is a locating-dominating set of G if for each v ∈ V(G) \ S, there exists w ∈ S such tha vw ∈ E(G) and NG(x) ∩ S= NG(y)∩S for any distinct vertices x and y in V(G) \ S. S is a stable locating-dominating set of G if it is a locating-dominating set of G and S \ {v} is a locating-dominating set of G for each v ∈ S. The minimum cardinality of a stable locating-dominating set of G, denoted by γsl(G), is called the stable locating-domination number of G. In this paper, we investigate this concept and the corresponding parameter for some graphs. Further, we introduce other related concepts and use them to characterize the stable locating-dominating sets in some graphs. Eman Camad Ahmad Gina Alquiza Malacas Sergio Jr. Rosales Canoy Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 638 649 10.29020/nybg.ejpam.v14i3.3998 Mixed Type Algorithms for Asymptotically Nonexpansive Mappings in Hyperbolic Spaces https://jalgstat.com/index.php/ejpam/article/view/4005 In this paper, a new mixed type iteration process for approximating a common fixed point of two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings is constructed. We then establish a strong convergence theorem under mild conditions in a uniformly convex hyperbolic space. The results presented here extend and improve some related results in the literature. Tanakit Thianwan Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 650 665 10.29020/nybg.ejpam.v14i3.4005 Asymptotic Approximations of Apostol-Genocchi Numbers and Polynomials https://jalgstat.com/index.php/ejpam/article/view/3976 <p>Asymptotic approximations of the Apostol-Genocchi numbers and<br />polynomials are derived using Fourier series and ordering of poles of<br />the generating function. Asymptotic formulas for the Apostol-Euler<br />numbers and polynomials are obtained as consequence. Asymptotic<br />formulas for special cases which include the Genocchi numbers and<br />polynomials are also explicitly stated.</p> Cristina Bordaje Corcino Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 666 684 10.29020/nybg.ejpam.v14i3.3976 Cyclic Codes from a Sequence over Finite Fields https://jalgstat.com/index.php/ejpam/article/view/3907 A cyclic code has been one of the most active research topics in coding theory because they have many applications in data storage systems and communication systems. They have efficient encoding and decoding algorithms. This paper explains the construction of a family of cyclic codes from sequences generated by a trace of a monomial over finite fields of odd characteristics. The parameter and some examples of the codes are presented in this paper. Nopendri Nopendri Intan Muchtadi-Alamsyah Djoko Suprijanto Aleams Barra Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 685 694 10.29020/nybg.ejpam.v14i3.3907 On a Topological Space Generated by Monophonic Eccentric Neighborhoods of a Graph https://jalgstat.com/index.php/ejpam/article/view/3990 <p>In this paper, we present a way of constructing a topology on a vertex set of a graph using monophonic eccentric neighborhoods of the graph <em>G. </em>In this type of construction, we characterize those graphs that induced the indiscrete topology, the discrete topology, and a particular point topology.</p> Anabel Enriquez Gamorez Sergio R. Canoy Jr. Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 695 705 10.29020/nybg.ejpam.v14i3.3990 A Finite Difference Fictitious Domain Wavelet Method for Solving Dirichlet Boundary Value Problem https://jalgstat.com/index.php/ejpam/article/view/3893 In this paper, we introduce a Finite Difference Fictitious Domain Wavelet Method (FDFDWM) for solving two dimensional (2D) linear elliptic partial differential equations (PDEs) with Dirichlet boundary conditions on regular geometric domain. The method reduces the 2D PDE into a 1D system of ordinary differential equations and applies a compactly supported wavelet to approximate the solution. The problem is embedded in a fictitious domain to aid the enforcement of the Dirichlet boundary conditions. We present numerical analysis and show that our method yields better approximation to the solution of the Dirichlet problem than traditional methods like the finite element and finite difference methods. Francis Ohene Boateng Joseph Ackora-Prah Benedict Barnes John Amoah-Mensah Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 706 722 10.29020/nybg.ejpam.v14i3.3893 Note on a Stieltjes Transform in terms of the Lerch Function https://jalgstat.com/index.php/ejpam/article/view/3991 <p>In this work the authors derive the Stieltjes transform of the logarithmic function in terms of the Lerch function. This transform is used to derive closed form solutions involving fundamental constants and special functions. Specifically we derive the definite integral given by</p><p><br />\[<br />\int_{0}^{\infty} \frac{(1-b x)^m \log ^k(c (1-b x))+(b x+1)^m \log ^k(c (b x+1))}{a+x^2}dx<br />\]<br /><br />where $a,b,c,m$ and $k$ are general complex numbers subject to the restrictions given in connection with the formulas.</p> Robert Reynolds Allan Stauffer Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 723 736 10.29020/nybg.ejpam.v14i3.3991 Fuzzy Translation and Fuzzy multiplication in BRK-algebras https://jalgstat.com/index.php/ejpam/article/view/3971 <p>In this paper, the concepts of fuzzy translation and fuzzy multiplication on a BRK-algebra are introduced. We investigated fuzzy translation and fuzzy multiplication (<em>BRK</em>-subalgebras &amp; <em>BRK</em>-ideals) in <em>BRK</em>-algebras and discussed related properties. Finally, we presented the nation fuzzy magnified--translation on <em>BRK</em>-algebra.</p> Halimah Abdulrahman Alshehri Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 737 745 10.29020/nybg.ejpam.v14i3.3971 Hankel Transform of the First Form (q,r)-Dowling Numbers https://jalgstat.com/index.php/ejpam/article/view/3953 <div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>In this paper, the Hankel transform of the generalized </span><span>q</span><span>-exponential polynomial of the first form (</span><span>q, r</span><span>)-Whitney numbers of the second kind is established using the method of Cigler. Consequently, the Hankel trans- form of the first form (</span><span>q, r</span><span>)-Dowling numbers is obtained as special case.</span></p></div></div></div> Roberto Bagsarsa Corcino Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 746 759 10.29020/nybg.ejpam.v14i3.3953 A View on Connectedness and Compactness in Fuzzy Soft Bitopological Spaces https://jalgstat.com/index.php/ejpam/article/view/3980 <p>In the present paper, we introduce the notions of (1, 2)∗-fuzzy soft b-separated sets, (1, 2)∗-fuzzy soft b-connectedness and (1, 2)∗-fuzzy soft b-compactness in fuzzy soft bitopological spaces. Then, some basic topological properties of these notions are investigated. Also, some illustrative examples are given to show the importance of the obtained theorems.</p> Abdelhamied Farrag Sayed Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 760 772 10.29020/nybg.ejpam.v14i3.3980 On 2-Resolving Sets in the Join and Corona of Graphs https://jalgstat.com/index.php/ejpam/article/view/3977 <p>Let G be a connected graph. An ordered set of vertices {v1, ..., vl} is a 2-resolving set in G if, for any distinct vertices u, w ∈ V (G), the lists of distances (dG(u, v1), ..., dG(u, vl)) and (dG(w, v1), ..., dG(w, vl)) differ in at least 2 positions. If G has a 2-resolving set, we denote the least size of a 2-resolving set by dim2(G), the 2-metric dimension of G. A 2-resolving set of size dim2(G) is called a 2-metric basis for G. This study deals with the concept of 2-resolving set of a graph. It characterizes the 2-resolving set in the join and corona of graphs and determine the<br />exact values of the 2-metric dimension of these graphs.</p> Jean Mansanadez Cabaro Helen Rara Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 773 782 10.29020/nybg.ejpam.v14i3.3977 Bessel type transform associated with Titchmarsh’s Theorem https://jalgstat.com/index.php/ejpam/article/view/3986 In this paper we have extended Titchmarsh’s theorem for the Bessel type transform for function on half-line [0, ∞) in a weighted Lp− metric are studied with the use of Bessel type generalized translation Balasaheb Bhagaji Waphare Yashoda S. Sindhe Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 783 787 10.29020/nybg.ejpam.v14i3.3986 A Note on the Definite Integral of the Lerch Function https://jalgstat.com/index.php/ejpam/article/view/4030 This is a compilation of definite integrals involving the Lerch, Polylogarithm, Hurwitz functions and fundamental constants. Connections to previous work is compared and discussed. This collection of definite integrals is new in current literature. Robert Reynolds Allan Stauffer Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 788 802 10.29020/nybg.ejpam.v14i3.4030 Total Perfect Hop Domination in Graphs Under Some Binary Operations https://jalgstat.com/index.php/ejpam/article/view/3975 <p>Let G = (V (G), E(G)) be a simple graph. A set S ⊆ V (G) is a perfect hop dominating set of G if for every v ∈ V (G) \ S, there is exactly one vertex u ∈ S such that dG(u, v) = 2. The smallest cardinality of a perfect hop dominating set of G is called the perfect hop domination number of G, denoted by γph(G). A perfect hop dominating set S ⊆ V (G) is called a total perfect hop dominating set of G if for every v ∈ V (G), there is exactly one vertex u ∈ S such that dG(u, v) = 2. The total perfect hop domination number of G, denoted by γtph(G), is the smallest cardinality of a total perfect hop dominating set of G. Any total perfect hop dominating set of G of cardinality γtph(G) is referred to as a γtph-set of G. In this paper, we characterize the total perfect hop dominating sets in the join, corona and lexicographic product of graphs and determine their corresponding total perfect hop domination number.</p> Raicah Cayongcat Rakim Helen M Rara Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 803 815 10.29020/nybg.ejpam.v14i3.3975 An Application of Finite Groups to Hopf algebras https://jalgstat.com/index.php/ejpam/article/view/3979 <p>Kaplansky’s famous conjectures about generalizing results from groups to Hopf al-<br />gebras inspired many mathematicians to try to find solusions for them. Recently, Cohen and Westreich in [8] and [10] have generalized the concepts of nilpotency and solvability of groups to Hopf algebras under certain conditions and proved interesting results. In this article, we follow their work and give a detailed example by considering a finite group G and an algebraically closed field K. In more details, we construct the group Hopf algebra H = KG and examine its properties to see what of the properties of the original finite group can be carried out in the case of H.</p> Tahani Al-Mutairi Mohammed Mosa Al-shomrani Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 816 828 10.29020/nybg.ejpam.v14i3.3979 Resolving Restrained Domination in Graphs https://jalgstat.com/index.php/ejpam/article/view/3985 <p>Let G be a connected graph. Brigham et al. [3] defined a resolving dominating set<br />as a set S of vertices of a connected graph G that is both resolving and dominating. A set S ⊆ V (G) is a resolving restrained dominating set of G if S is a resolving dominating set of G and S = V (G) or hV (G) \ Si has no isolated vertex. In this paper, we characterize the resolving restrained dominating sets in the join, corona and lexicographic product of graphs and determine the resolving restrained domination number of these graphs.</p> Gerald Bacon Monsanto Helen M. Rara Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 829 841 10.29020/nybg.ejpam.v14i3.3985 Laplace-SBA Method for Solving Nonlinear Coupled Burger's Equations https://jalgstat.com/index.php/ejpam/article/view/3932 <p>Burger’s equations, an extension of fluid dynamics equations, are typically solved by several numerical methods. In this article, the laplace-Somé Blaise Abbo method is used to solve nonlinear Burger equations. This method is based on the combination of the laplace transform and the SBA method. After reminders of the laplace transform, the basic principles of the SBA method are described. The process of calculating the Laplace-SBA algorithm for determining the exact solution of a linear or nonlinear partial derivative equation is shown. Thus, three examples<br />of PDE are solved by this method, which all lead to exact solutions. Our results suggest that this method can be extended to other more complex PDEs.</p> Joseph Bonazebi-Yindoula Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 842 862 10.29020/nybg.ejpam.v14i3.3932 New Generalized Hermite−Hadamard Type Inequalities for p−convex Functions in the Mixed Kind https://jalgstat.com/index.php/ejpam/article/view/4015 <p>In this article, we would like to state generalized results related to well-known Hermite− Hadamard dual inequality for p−convex functions using the newly introduced notion of (s, r)−convexity (s−convex function in mixed kind) with different techniques. Hence various established and new results would be captured as special case.</p> Muhammad Bilal Asif R. Khan Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 863 880 10.29020/nybg.ejpam.v14i3.4015 On the Operator ⊕k,m Related to the Wave Equation and Laplacian https://jalgstat.com/index.php/ejpam/article/view/4006 <pre>In this article, we study the fundamental solution of the operator </pre><pre><span>$\oplus _{m}^{k}$</span>, iterated <span>$k$</span>-times and is defined by</pre><pre><span>$$</span></pre><pre><span>\oplus _{m}^{k}</span></pre><pre><span> = \left[\left(\sum_{r=1}^{p} \frac{\partial^2}</span></pre><pre><span> {\partial x_r^2}+m^{2}\right)^4 - \left( \sum_{j=p+1}^{p+q}</span></pre><pre><span> \frac{\partial^2}{\partial x_{j}^2} \right)^4 \right ]^k,</span></pre><pre><span>$$</span> </pre><pre>where <span>$m$</span> is a <span>nonnegative</span> real number, <span>$p+q=n$</span> is the dimension of the Euclidean space <span>$\mathbb{R}^n$</span>,</pre><pre><span>$x=(x_1,x_2,\ldots,x_n)\in\mathbb{R}^n$</span>, <span>$k$</span> is a <span>nonnegative</span> integer. At first we study the fundamental solution of the operator <span>$\oplus _{m}^{k}$</span> and after that, we apply such the fundamental solution to solve for the solution of the equation <span>$\oplus _{m}^{k}u(x)= f(x)$</span>, where <span>$f(x)$</span> is generalized function and <span>$u(x)$</span> is unknown function for <span>$ x\in \mathbb{R}^{n}$</span>.</pre> Sudprathai Bupasiri Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 881 894 10.29020/nybg.ejpam.v14i3.4006 Introduction to Neutrosophic B-algebras https://jalgstat.com/index.php/ejpam/article/view/3996 <p>This paper introduces the notion of neutrosophic B-algebra. Several results on properties of neutrosophic B-algebras and neutrosophic subalgebras are presented and proved.</p> Danilo Oppus Jacobe Jocelyn P. Vilela Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 895 904 10.29020/nybg.ejpam.v14i3.3996 Group Splitting with SOR/AOR Methods for Solving Boundary Value Problems: A Computational Comparison https://jalgstat.com/index.php/ejpam/article/view/4031 <p>Many researchers are working on the explicit group methods as the alternative methods for solving several boundary value problems. These methods have been shown to be much faster than the other point iterative methods in solving the elliptic partial differential equations (EPDEs), which is due to the formers’ overall lower computational complexities. This paper is concerned with the application of a suitable Explicit Group (EG) iterative method for solving EPDEs. This study will compare several iterative methods such that S5-point-SOR,4 Point-EGSOR, 5S-point-AOR, and 4 Point-EGAOR. Numerical experiments were carried out to confirm our results by using MATLAB software. The results reveal that 4 Point-EGAOR is the most superior method among these methods.</p> Abdulkafi Mohammed Saeed Najah Mohammad AL-harbi Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 905 914 10.29020/nybg.ejpam.v14i3.4031 Note on (i, j) − mX − β−Exterior Sets in Biminimal 3 Structure Spaces https://jalgstat.com/index.php/ejpam/article/view/4003 <p>In that paper, the concept of (i, j) − mX − β−exterior sets in a biminimal structure<br />space (BSS) and a biminimal structure subspace (BSs) were introduced. Based on properties of BSS and BSs, some new notions and several properties of those sets dealing with this space were obtained in both of BSS and BSs. Some examples were given to illustrate the effectiveness of these results.</p> Torsak Prasertsang Patarawadee Prasertsang Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 915 922 10.29020/nybg.ejpam.v14i3.4003 Some New Results of Fixed Point in Fuzzy Soft G-metric Spaces https://jalgstat.com/index.php/ejpam/article/view/4028 The main goal of the present paper is to study and prove some results of fixed<br />points for mappings satisfying different conditions in fuzzy soft G-metric spaces. Abdelhamied Farrag Sayed Abdullah Alahmari Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 923 941 10.29020/nybg.ejpam.v14i3.4028 Tensor Product and Certain Solutions of Fractional Wave Type Equation https://jalgstat.com/index.php/ejpam/article/view/4012 In this paper we Önd certain solutions of some fractional partial di§erential equations. Tensor product of Banach spaces is used to Önd some solutions where separation of variables does not work. We solve the fractional wave type equation using fractional Fourier Series Ibtisam Benkemache Mohammad Al-horani Roshdi Rashid Khalil Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 942 948 10.29020/nybg.ejpam.v14i3.4012 On the Aspects of Enriched Lattice-valued Topological Groups and Closure of Lattice-valued Subgroups https://jalgstat.com/index.php/ejpam/article/view/4021 <p>Starting with L as an enriched cl-premonoid, in this paper, we explore some categorical connections between L-valued topological groups and Kent convergence groups, where it is shown that every L-valued topological group determines a well-known Kent convergence group, and conversely, every Kent convergence group induces an L-valued topological group. Considering an L-valued subgroup of a group, we show that the category of L-valued groups, L-GRP has initial structure. Furthermore, we consider a category L-CLS of L-valued closure spaces, obtaining its relation with L-valued Moore closure, and provide examples in relation to L-valued subgroups that produce Moore collection. Here we look at a category of L-valued closure groups, L-CLGRP proving that it is a topological category. Finally, we obtain a relationship between L-GRP and L-TransTOLGRP, the category of L-transitive tolerance groups besides adding some properties of L-valued closures of L-valued subgroups on L-valued topological groups.</p> TMG Ahsanullah Fawzi Al-Thukair Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 949 968 10.29020/nybg.ejpam.v14i3.4021 Generalized Iteration Method via Green's Function for the Solution of the Fourth-order Boundary Value Problems https://jalgstat.com/index.php/ejpam/article/view/4020 <p>The aim of this paper is to extend and generalize Picard-Green’s fixed point iteration method for the solution of fourth-order Boundary Value Problems. Several numerical applications to linear and nonlinear fourth-order Boundary Value Problems are discussed to illustrate the main results.</p> Fatma Aydın Akgün Zaur Rasulov Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 969 979 10.29020/nybg.ejpam.v14i3.4020 Definite Integral of Power and Algebraic Functions in terms of the Lerch Function https://jalgstat.com/index.php/ejpam/article/view/4017 <p>Bierens de haan (1867) evaluated a definite integral involving the cotangent function and this result was also listed in Gradshteyn and Ryzhik (2007). The objective of this present note is to use this integral along with Cauchy's integral formula to derive a definite logarithmic integral in terms of the Lerch function. We will use this integral formula to produce a table of known and new results in terms of special functions and thereby expanding the list of definite integrals in both text books.</p> Robert Reynolds Allan Stauffer Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 980 988 10.29020/nybg.ejpam.v14i3.4017 On Gamma LA-Rings and Gamma LA-Semirings https://jalgstat.com/index.php/ejpam/article/view/4034 <p>In this note, first we add some new results in Gamma LA-rings and then we initiate the notion of Γ-LA-semirings. Moreover, we introduce and discuss the terms left ideals, right ideals, bi-ideal, quasi ideals, almost prime and weakly almost prime ideals of a Γ-LA-semiring and their characterizations.</p> Waheed Ahmad Khan Abdelghani Taouti Azar Salami Zahid Hussain Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 989 1001 10.29020/nybg.ejpam.v14i3.4034 Finite Groups with Minimal CSS-subgroups https://jalgstat.com/index.php/ejpam/article/view/4036 Let G be a finite group. A subgroup H of G is called SS-quasinormal in G if there is a supplement B of H to G such that H permutes with every Sylow subgroup of B. A subgroup H of G is called CSS-subgroup in G if there exists a normal subgroup K of G such that G = HK and H ∩K is SS-quasinormal in G. In this paper, we investigate the influence of minimal CSS-subgroups of G on its structure. Our results improve and generalize several recent results in the literature. A. A. Heliel R. A. Hijazi S. M. Al-Shammari Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 1002 1014 10.29020/nybg.ejpam.v14i3.4036 On Resolving Hop Domination in Graphs https://jalgstat.com/index.php/ejpam/article/view/4055 <p>A set S of vertices in a connected graph G is a resolving hop dominating set of G if S is a resolving set in G and for every vertex v ∈ V (G) \ S there exists u ∈ S such that dG(u, v) = 2. The smallest cardinality of such a set S is called the resolving hop domination number of G. This paper presents the characterizations of the resolving hop dominating sets in the join, corona and lexicographic product of two graphs and determines the exact values of their corresponding resolving hop domination number.</p> Jerson Saguin Mohamad Helen M. Rara Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 1015 1023 10.29020/nybg.ejpam.v14i3.4055 On General Properties of Degenerate Systems of Second Order Partial Differential Equations of Hypergeometric Type https://jalgstat.com/index.php/ejpam/article/view/4016 <p>For the first time, the general properties of degenerate related hypergeometric systems such as Horn, Whittaker, Bessel and Laguerre are investigated together. The joint research allowed to reveal their various common properties and to establish a number of new degenerate related systems. They are all private cases of the common system offered by the authors for consideration. For the full study, it is important to classify its regular and irregular special curves and to identify the types of corresponding solutions. In this paper, they are implemented using simple rules. Special attention is paid to the construction of normal and regular solutions, because the solutions of all related degenerate systems such as Horn, Whittaker, Bessel and Laguerre near the irregular singularity on infinity relate to this species. Peculiarities of building normal-regular solutions by the Frobenius-Latysheva method are shown. All constructed normal-regular solutions are expressed through the function of Humbert  variables, which is the solution of degenerate hypergeometric system of Horn type. As an example, the cases  where, along with the application of the Frobenius-Latysheva method, the possibility of outputting new degenerate related systems is demonstrated.</p> Akkenzhe Issenova Zhaksylyk Tasmambetov Nusrat Rajabov Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 1024 1043 10.29020/nybg.ejpam.v14i3.4016 Comparison of the Adomian Decomposition Method and Regular Perturbation Method on Nonlinear Equations Second Kind of Volterra https://jalgstat.com/index.php/ejpam/article/view/4014 <p>In this paper, we study convergence of Adomian decomposition method applied to<br />second kind Volterra general integral and show that this method and regular perturbation method converges to the same solution.</p> Rasmane Yaro Bakari Abbo Bassono Francis Youssouf Pare Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 1044 1056 10.29020/nybg.ejpam.v14i3.4014 Extremal Copulas and Tail Dependence in Modeling Stochastic Financial Risk https://jalgstat.com/index.php/ejpam/article/view/3951 <p>These last years the stochastic modeling became essential in financial risk management related to the ownership and valuation of financial products such as assets, options and bonds. This paper presents a contribution to the modeling of stochastic risks in finance by using both extensions of tail dependence coefficients and extremal dependance structures based on copulas. In particular, we show that when the stochastic behavior of a set of risks can be modeled by a multivariate extremal process a corresponding form of the underlying copula describing their<br />dependence is determined. Moreover a new tail dependence measure is proposed and properties of this measure are established.</p> Hassane Abba Mallam Natatou Dodo Moutari Barro Diakarya Saley Bisso Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 1057 1081 10.29020/nybg.ejpam.v14i3.3951 Quantum Codes Obtained through Constacyclic Codes over Z3 + νZ3 + ωZ3 + νωZ3 https://jalgstat.com/index.php/ejpam/article/view/4043 This paper is concerned with, structural properties and construction of quantum codes over Z3 by using constacyclic codes over the finite commutative non-chain ring R = Z3 + νZ3 + ωZ3 + νωZ3 where ν2 = 1, ω2 = ω, νω = νω, and Z3 is field having 3 elements with characteristic 3. A Gray map is defined between R and Z43. The parameters of quantum codes over Z3 are obtained by decomposing constacyclic codes into cyclic and negacyclic codes over Z3. As an application, some examples of quantum codes of arbitrary length, are also obtained. Jagbir Singh Prateek Mor Shikha . Meena . Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 1082 1097 10.29020/nybg.ejpam.v14i3.4043 Forcing Total dr-Power Domination Number of Graphs Under Some Binary Operations https://jalgstat.com/index.php/ejpam/article/view/3915 In this paper, the total dr-power domination number of graphs such as complete bipartite graph, generalized fan and generalized wheel are obtained. The forcing total dr-power domination number of graphs resulting from some binary operations such as join, corona and lexicographic product of graphs were determined. Cris Laquibla Armada Copyright (c) 2021 European Journal of Pure and Applied Mathematics 2021-08-05 2021-08-05 14 3 1098 1107 10.29020/nybg.ejpam.v14i3.3915