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Latest Published Articles

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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Study on data transmission problem from the existence of Hamiltonian fractional factor

OMS-Vol. 3 (2019), Issue 1, pp. 49–58 Open Access Full-Text PDF
Jianzhang Wu, Jiabin Yuan, Wei Gao
Abstract:In the field of computer networks, the performance of data transmission is usually characterized by the fractional factor. Some sufficient conditions for the existence of Hamilton fractional factors are obtained in this paper, and they extend the original theory presented in Gao et al. [1].
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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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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory
BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC