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Latest Published Articles

Global existence, uniqueness, and asymptotic behavior of solution for the Euler-Bernoulli viscoelastic equation

OMA-Vol. 3 (2019), Issue 1, pp. 42–51 Open Access Full-Text PDF
Mohamed Mellah, Ali Hakem
Abstract: We study the global existence and uniqueness of a solution to an initial boundary value problem for the Euler-Bernoulli viscoelastic equation \(u_{tt}+\Delta^{2}u-g_{1}\ast\Delta^{2} u+g_{2}\ast\Delta u+u_{t}=0.\) Further, the asymptotic behavior of solution is established.
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The outer-connected vertex edge domination number in Lexicographic product graphs

ODAM-Vol. 2 (2019), Issue 2, pp. 19–22 Open Access Full-Text PDF
Opeyemi Oyewumi, Abolape Deborah Akwu, Obakpo Johnson Ben
Abstract: An outer-connected vertex edge dominating set (OCVEDS) for an arbitrary graph \(G\) is a set \(D \subset V(G)\) such that \(D\) is a vertex edge dominating set and the graph \(G \setminus D\) is connected. The outer-connected vertex edge domination number of \(G\) is the cardinality of a minimum OCVEDS of \(G\), denoted by \(\gamma_{ve}^{oc}(G)\). In this paper, we give the outer-connected vertex edge dominating set in lexicographic product of graphs.
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Minimum degree polynomial of graphs obtained by some graph operators

ODAM-Vol. 2 (2019), Issue 2, pp. 1–18 Open Access Full-Text PDF
Bommanahal Basavanagoud, Praveen Jakkannavar
Abstract: The minimum degree matrix \(MD(G)\) of a graph \(G\) of order \(n\) is an \(n\times n\) symmetric matrix whose \((i,j)^{th}\) entry is \(min\{d_i,d_j\}\) whenever \(i\neq j\), and zero otherwise, where \(d_i\) and \(d_j\) are the degrees of the \(i^{th}\) and \(j^{th}\) vertices of \(G\), respectively. In the present work, we obtain the minimum degree polynomial of the graphs obtained by some graph operators (generalized \(xyz\)-point-line transformation graphs).
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Analysis of the qualitative behaviour of an eighth-order fractional difference equation

ODAM-Vol. 2 (2019), Issue 1, pp. 41–47 Open Access Full-Text PDF
Mohammed Bakheet Almatrafi, Marwa Mohammed Alzubaidi
Abstract: The exact solutions of most nonlinear difference equations cannot be obtained theoretically sometimes. Therefore, a massive number of researchers predict the long behaviour of most difference equations by investigating some qualitative behaviours of these equations from the governing equations. In this article, we aim to analyze the asymptotic stability, global stability, periodicity of the solution of an eighth-order difference equation. Moreover, a theoretical solution of a special case equation will be presented in this paper.
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Fractional frequency Laplace transform by inverse difference operator with shift value

OMS-Vol. 3 (2019), Issue 1, pp. 121–128 Open Access Full-Text PDF
Sandra Pinelas, Meganathan Murugesan, Britto Antony Xavier Gnanaprakasam
Abstract: In this paper, we study the outcome of fractional Laplace transform using inverse difference operator with shift value. By the definition of convolution product, the properties of fractional transformation, the relation between convolution product and fractional frequency Laplace transform with shift value have been discussed. Further, the connection between usual Laplace transform and fractional frequency Laplace transform with shift value are also presented. Numerical examples with graphs are verified and generated by MATLAB.
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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory
BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC