Commutators of fractional integral with variable kernel on variable exponent Herz-Morrey spaces

OMA-Vol. 3 (2019), Issue 1, pp. 19–29 Open Access Full-Text PDF
Afif Abdalmonem, Omer Abdalrhman, Hossam Eldeen Mohammed
Abstract: By using the boundedness results for the commutators of the fractional integral with variable kernel on variable Lebesgue spaces \(L^{p(\cdot)}(\mathbb{R}^{n})\), the boundedness results are established on variable exponent Herz-Morrey spaces \(M\dot{K}_{q,p(\cdot)}^{\alpha, \lambda}(\mathbb{R}^{n})\).
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Bounds on the covering radius of some classes of codes over \(\mathbb R\)

ODAM-Vol. 2 (2019), Issue 1, pp. 14–23 Open Access Full-Text PDF
P. Chella Pandian
Abstract: In this paper, the covering radius of codes over \(\mathbb R ={\mathbb Z_2}{R^{*}},\) where \(R^{*}={\mathbb Z_2}+v{\mathbb Z_2},v^{2}=v\) with different weight are discussed. The block repetition codes over \(\mathbb R\) is defined and the covering radius for block repetition codes, simplex code of \(\alpha\)-type and \(\beta\)-type in \(\mathbb R\) are obtained.
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Existence and uniqueness results for Navier problems with degenerated operators

OMA-Vol. 3 (2019), Issue 1, pp. 07–18 Open Access Full-Text PDF
Albo Carlos Cavalheiro
Abstract: In this article, we prove the existence and uniqueness of solutions for the Navier problem \( \Delta\big[\omega_1(x)\vert\Delta u\vert^{p-2}\Delta u+ \nu_1(x)\vert\Delta u\vert^{q-2}\Delta u\big] -{div}\big[\omega_2(x)\vert\nabla u\vert^{p-2}\nabla u +\nu_2(x)\vert\nabla u\vert^{s-2}\nabla u\big] = f(x) – { div}(G(x)),\) in \({\Omega},\) with
\(u(x) = {\Delta}u= 0,\) in \({\partial\Omega},\) where \(\Omega\) is a bounded open set of \(\mathbb{R}^N\) for \(N\geq 2\), \(\frac{f}{\omega_2}\in L^{p’}(\Omega , {\omega}_2)\) and \(\frac{G}{{\nu}_2}\in \left[L^{s’}(\Omega ,{\nu}_2)\right]^N\).
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Degree based graph invariants for the molecular graph of Bismuth Tri-Iodide

EASL-Vol. 2 (2019), Issue 1, pp. 01–11 Open Access Full-Text PDF
Zehui Shao, Abaid ur Rehman Virk, Muhammad Samar Javed, M. A. Rehman, Mohammad Reza Farahani
Abstract:In the fields of chemical graph theory (CGT), mathematical chemistry and molecular topology, a~topological index (TI) also known as a connectivity~index~is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. \(BiI_{3}\) is an excellent inorganic compound and is very useful in qualitative inorganic analysis and topological indices of \(BiI_{3}\) help to predict many properties like boiling point, heat of formation, strain energy, rigidity and fracture toughness and correlate the structure with various physical properties, chemical reactivity and biological activities. This paper computes several degree-based topological indices like multiplicative first Zagreb index, multiplicative second Zagreb index, multiplicative atomic bond connectivity index, multiplicative first and second hyper Zagreb index and multiplicative geometric arithmetic index for Bismuth Tri-Iodide chains and sheets.
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Asymptotic behavior of positive solutions of nonlinear fractional differential equations with Caputo-type Hadamard derivative

OMS-Vol. 3 (2019), Issue 1, pp. 40–48 Open Access Full-Text PDF
Said R. Grace, Shurong Sun, Zhenlai Han
Abstract:In this paper we are concerned with the problem of asymptotic integration of positive solutions of higher order fractional differential equations with Caputo-type Hadamard derivative of the form \(^{C,H}D_{a}^r x(t)=e(t)+f(t,x(t)), \; a>1,\) where \(r = n +\alpha -1, \alpha\in (0, 1), n \in \mathbb{Z}^+\). We shall apply our technique to investigate the oscillatory and asymptotic behavior of all solutions of the integral equation \(x(t)=e(t)+\int_a ^t (\ln\frac{t}{s} )^{r-1} k(t,s)f(s,x(s))\frac{ds}{s}, \; a>1,\) \(r\) is as above.
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Mathematical analysis of diarrhoea model with saturated incidence rate

OMS-Vol. 3 (2019), Issue 1, pp. 29–39 Open Access Full-Text PDF
Ebenezer Bonyah, Gratien Twagirumukiza, Patience Pokuaa Gambrah
Abstract:We present a compartmental mathematical model of (SITR) to investigate the effect of saturation treatment in the dynamical spread of diarrhea in the community. The mathematical analysis shows that the disease free and the endemic equilibrium points of the model exist. The disease-free equilibrium is locally and globally asymptotically stable when \(R_{0}<1\) and unstable otherwise \(R_{0}>1\). Numerical simulation results, show the effect of saturation treatment function on the spread of diarrhea. Efficacy of treatment shows a great impact in the total eradication of diarrhea epidemic.
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Stability of Pinelas-Septoicosic functional equation

OMS-Vol. 3 (2019), Issue 1, pp. 11–28 Open Access Full-Text PDF
Sandra Pinelas, Govindan Vediyappan, Kandhasamy Tamilvanan
Abstract:In this paper, we find the general solution of a Septoicosic functional equation (11) for all \(x, y \in X\) and investigate its general Hyers-Ulam stability in Banach Space using direct and fixed point methods.
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