Boundedness of fractional Marcinkiewicz integral with variable kernel on variable Morrey-Herz spaces

OMS-Vol. 2 (2018), Issue 1, pp. 93–114 | Open Access Full-Text PDF
Afif Abdalmonem, Omer Abdalrhman, Shuangping Tao
Abstract:In this article, the authors obtain the boundedness of the fractional Marcinkiewicz integral with variable kernel on Morrey-Herz spaces with variable exponents \(\alpha\) and \(p\). The corresponding boundedness for commutators generalized by the Lipschitz function is also considered.
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On a class of new hypergeometric transformations

OMS-Vol. 2 (2018), Issue 1, pp. 84–92 | Open Access Full-Text PDF
Giovanni Mingari Scarpello, Daniele Ritelli
Abstract:In this article we continue the investigations presented in our previous papers [1,2,3,4], presenting some, for the best of our knowledge, new transformations of the Gauss hypergeometric function (3) and (13). They have been obtained using only elementary methods and stem from a couple of integrals evaluated in terms of complete elliptic integral of first kind by Legendre in [5] Chapter XXVII, at sections II and III.
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Wiener polarity index of quasi-tree molecular structures

OMS-Vol. 2 (2018), Issue 1, pp. 73–83 | Open Access Full-Text PDF
Zihao Tang, Li Liang, Wei Gao
Abstract:As an important branch of theoretical chemistry, chemical index calculation has received wide attention in recent years. Its theoretical results have been widely used in many fields such as chemistry, pharmacy, physics, biology, materials, etc. and play a key role in reverse engineering. Its basic idea is to obtain compound characteristics indirectly through the calculation of topological index. As a basic structure, quasi-tree structures are widely found in compounds. In this paper, we obtain the maximal value and the second smallest value of quasi-tree graphs of order \(n.\)
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Fixed point results for the complex fractal generation in the S -iteration orbit with s -convexity

OMS-Vol. 2 (2018), Issue 1, pp. 56–72 | Open Access Full-Text PDF
Krzysztof Gdawiec, Abdul Aziz Shahid
Abstract:Since the introduction of complex fractals by Mandelbrot they gained much attention by the researchers. One of the most studied complex fractals are Mandelbrot and Julia sets. In the literature one can find many generalizations of those sets. One of such generalizations is the use of the results from fixed point theory. In this paper we introduce in the generation process of Mandelbrot and Julia sets a combination of the S-iteration, known from the fixed point theory, and the s-convex combination. We derive the escape criteria needed in the generation process of those fractals and present some graphical examples.
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On the viscosity rule for common fixed points of two nonexpansive mappings in CAT(0) spaces

OMS-Vol. 2 (2018), Issue 1, pp. 39–55 | Open Access Full-Text PDF
Ebenezer Bonyah, Maqbool Ahmad, Iftikhar Ahmad
Abstract:In this paper, we establish viscosity rule for common fixed points of two nonexpansive mappings in the framework of CAT(0) spaces. The strong convergence theorems of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. The results presented in this work extend and improve some recent announced in the literature.
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Combination of Homotopy Perturbation Method (HPM) and Double Sumudu Transform to Solve Fractional KdV Equations

OMS-Vol. 2 (2018), Issue 1, pp. 29–38 | Open Access Full-Text PDF
Hamood ur Rehman, Muhammad Shoaib Saleem, Ayesha Ahmad
Abstract:In this work, we developed homotopy perturbation double Sumudu transform method (HPDSTM) which is obtained by combining homotopy perturbation method, double Sumudu transform and He’s polynomials. The method is applied to find the solution of linear fractional one and two dimensional dispersive KdV and nonlinear fractional KdV equations to illustrate the reliability of the method. It is observed that the solutions obtained by the method converge rapidly to the exact solutions. This method is very powerful, and professional techniques for solving different kinds of linear and nonlinear fractional order differential equations.
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Hyper Zagreb Index of Bridge and Chain Graphs

OMS-Vol. 2 (2018), Issue 1, pp. 1–17 | Open Access Full-Text PDF
Nilanjan De
Abstract:Let \(G\) be a simple connected molecular graph with vertex set \(V(G)\) and edge set \(E(G)\). One important modification of classical Zagreb index, called hyper Zagreb index \(HM(G)\) is defined as the sum of squares of the degree sum of the adjacent vertices, that is, sum of the terms \({[{{d}_{G}}(u)+{{d}_{G}}(v)]^2}\) over all the edges of \(G\), where \(d_G(v)\) denote the degree of the vertex \(u\) of \(G\). In this paper, the hyper Zagreb index of certain bridge and chain graphs are computed and hence using the derived results we compute the hyper Zagreb index of several classes of chemical graphs and nanostructures.
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MHD couette and poiseuille flow of a third grade fluid

OMA-Vol. 1 (2017), Issue 2, pp. 01–19 | Open Access Full-Text PDF
Mohsin Kamran, Imran Saddique
Abstract:The main theme of this work is to apply the Adomian decomposition method (ADM) to solve the non-linear differential equations which arise in fluid mechanics. we study some steady unidirectional magnetohydrodynamics (MHD) flow problems namely, Couette flow, Poiseuille flow and Generalized-Couette flow of a third grade non Newtonian fluid between two horizontal infinite parallel plates in the presence of a transversal magnetic field. Moreover, the MHD solutions for a Newtonian fluid, as well as those corresponding to a third grade fluid are obtained by the limiting cases of our solutions. Finally, the influence of the pertinent parameters on the velocity of fluids is also analyzed by graphical illustrations.
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Forgotten polynomial and forgotten index of certain interconnection networks

OMA-Vol. 1 (2017), Issue 1, pp. 44–59 | Open Access Full-Text PDF
Hajra Siddiqui, Mohammad Reza Farahani
Abstract: Chemical reaction network theory is an area of applied mathematics that attempts to model the behavior of real world chemical systems. Since its foundation in the 1960s, it has attracted a growing research community, mainly due to its applications in biochemistry and theoretical chemistry. It has also attracted interest from pure mathematicians due to the interesting problems that arise from the mathematical structures involved. It is experimentally proved that many properties of the chemical compounds and their topological indices are correlated. In this report, we compute closed form of forgotten polynomial and forgotten index for interconnection networks. Moreover we give graphs to see dependence of our results on the parameters of structures.
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