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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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Flow of viscous fluid over an infinite plate with Caputo-Fabrizio derivatives

OMS-Vol. 3 (2019), Issue 1, pp. 115–120 Open Access Full-Text PDF
M. Umar Farooq, M. Saqib Khan, Ahmad Hajizadeh
Abstract: This paper presents Caputo-Fabrizio fractional derivatives approach to analysis of a viscous fluid over an infinite flat plate together with general boundary motion. Closed form exact general solutions of the fluid velocity are obtained by means of the Laplace transform. The solutions of ordinary viscous fluids corresponding to time-derivatives of integer order is obtained as particular cases of the present solutions. Several special cases are also discussed. Numerical computations and graphical illustrations are used in order to study the effects of the Caputo-Fabrizio time-fractional parameter \(\alpha\) and Reynolds number on velocity field.
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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory
BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC