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Latest Published Articles

Effect of filler on solid insulator surface and tracking length in high voltage systems

EASL-Vol. 2 (2019), Issue 2, pp. 37-42 Open Access Full-Text PDF
Irfanullah Khan, Muhammad Ahtasham Abid, Zahid Ullah, Arooj Rashid
Abstract: This paper presents the effect of different fillers on tracking length of electrical insulators. Insulator samples were prepared using polyester resin-c and were tested according to ASTM D2302. A standard test known as “Inclined plane test” is used to test the insulators after the application of high stresses. Track length of each sample is measured using a Polari scope. Track length of filler added insulators is compared to the insulator without filler and a significant change was noted among them.
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Multilinear fractional integral with rough kernel on variable exponent Morrey-Herz spaces

OMS-Vol. 3 (2019), Issue 1, pp. 167-183 Open Access Full-Text PDF
Afif Abdalmonem, Omer Abdalrhman, Shuangping Tao
Abstract: In this article, we study a class of the multilinear fractional integral with rough kernel on Morrey-Herz space with \(p(\cdot), q(\cdot), \alpha(\cdot).\) By using the properties of the variable exponent spaces, the boundedness of the multilinear fractional integral operator is obtained on variable nonhomogeneous Morrey-Herz spaces \({MK}_{q(\cdot),p(\cdot)}^{\alpha(\cdot),\lambda}(\mathbb{R}^{n}).\)
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First analytic solution for the oscillatory flow of a Maxwell’s fluid with annulus

OMS-Vol. 3 (2019), Issue 1, pp. 159-166 Open Access Full-Text PDF
Chaudry Masood Khalique, Rabia Safdar, Madeeha Tahir
Abstract: The major purpose of this article is to discuss the oscillatory flow of an incompressible viscous Maxwell fluids (IVMF) between two infinite coaxial of circular pipes. In the case when time \(t=0\) the inner pipe is lying at rest where as at \(t>0\) the inner pipe of the annulus starts to oscillate along the common axis of the pipes. The analytical solutions of the problem are obtained via integral transformation technique which is beneficial for time dependent problems. Moreover, the derived solutions are given under the series form of the generalized \(G\) functions satisfying all the imposed auxiliary conditions whereas, the solutions for ordinary Maxwell and Newtonian fluids appear as the limiting case of the present obtained results. We include graphical comparison between Maxwell and Newtonian fluid, and we also explored the effects of different physical parameters on the fluid motion.
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Positive solutions for nonlinear Caputo-Hadamard fractional differential equations with integral boundary conditions

OMA-Vol. 3 (2019), Issue 1, pp. 61-69 Open Access Full-Text PDF
Abdelouaheb Ardjouni, Ahcene Djoudi
Abstract: We study the existence and uniqueness of positive solutions of the nonlinear fractional differential equation with integral boundary conditions \(\mathfrak{D}_{1}^{\alpha }x\left( t\right) =f\left( t,x\left( t\right) \right) ,\;\;\; 1<t\leq e, x\left( 1\right) =\lambda \int_{1}^{e}x\left( s\right) ds+d,\) where  \(\mathfrak{D}_{1}^{\alpha }\) is the Caputo-Hadamard fractional derivative of order \(0<\alpha \leq 1\). In the process we convert the given fractional differential equation into an equivalent integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem and the method of upper and lower solutions to show the existence of a positive solution of this equation. We also use the Banach fixed point theorem to show the existence of a unique positive solution. Finally, an example is given to illustrate our results.
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Solutions structures for some systems of fractional difference equations

OMA-Vol. 3 (2019), Issue 1, pp. 51-61 Open Access Full-Text PDF
M. B. Almatrafi
Abstract: It is a well-known fact that the majority of rational difference equations cannot be solved theoretically. As a result, some scientific experts use manual iterations to obtain the exact solutions of some of these equations. In this paper, we obtain the fractional solutions of the following systems of difference equations:
$$
x_{n+1}=\frac{x_{n-1}y_{n-3}}{y_{n-1}\left( -1-x_{n-1}y_{n-3}\right) },\ \ \
y_{n+1}=\frac{y_{n-1}x_{n-3}}{x_{n-1}\left( \pm 1\pm y_{n-1}x_{n-3}\right) }
,\ \ \ n=0,1,…,
$$
where the initial data \(x_{-3},\ x_{-2},\ x_{-1},\ \)\ \(
x_{0},\ y_{-3},\ y_{-2},\ y_{-1}\) and \(\ \ y_{0}\;\) are arbitrary non-zero real numbers. All solutions will be depicted under specific initial conditions.
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Magnetohydrodynamic flow of dissipative casson-carreau nanofluid over a stretching sheet embedded in a porous medium under the influence of thermal radiation and variable internal heat generation

EASL-Vol. 2 (2019), Issue 2, pp. 18-36 Open Access Full-Text PDF
Gbeminiyi Sobamowo, O. A. Adesina, Lawrence Jayesimi
Abstract: In this paper, finite difference method is used to study the combined effects of thermal radiation, inclined magnetic field and temperature-dependent internal heat generation on unsteady two-dimensional flow and heat transfer analysis of dissipative Casson-Carreau nanofluid over a stretching sheet embedded in a porous medium. In the study, kerosene is used as the base fluid which is embedded with the silver (Ag) and copper (Cu) nanoparticles. Also, effects of other pertinent parameters on the flow and heat transfer characteristics of the Casson-Carreau nanofluids are investigated and discussed. From the results, it is established that the temperature field and the thermal boundary layers of Ag-Kerosene nanofluid are highly effective when compared with the Cu-Kerosene nanofluid. Heat transfer rate is enhanced by increasing power-law index and unsteadiness parameter. Skin friction coefficient and local Nusselt number can be reduced by magnetic field parameter and they can be enhanced by increasing the aligned angle. Friction factor is depreciated and the rate of heat transfer increases by increasing the Weissenberg number. A very good agreement is established between the results of the present study and the previous results. The present analysis can help in expanding the understanding of the thermo-fluidic behaviour of the Casson-Carreau nanofluid over a stretching sheet.
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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory
BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC