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.
Read more

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.
Read more

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.
Read more

Weaker form of totally continuous functions

OMS-Vol. 3 (2019), Issue 1, pp. 01–06 Open Access Full-Text PDF
Md. Hanif Page and Lakshmi Narayan Mishra
Abstract:The objective of this paper is to study new type of continuous functions called totally \(\alpha\)gs-continuous functions using $\alpha$gs-open sets. Furthermore we discuss covering properties and obtain their characterizations by including counter examples.
Read more

Higher order nonlinear equation solvers and their dynamical behavior

OMA-Vol. 2 (2018), Issue 2, pp. 172–193 | Open Access Full-Text PDF
Sabir Yasin, Amir Naseem
Abstract:In this report we present new sixth order iterative methods for solving non-linear equations. The derivation of these methods is purely based on variational iteration technique. To check the validity and efficiency we compare of methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method by solving some test examples. Numerical results shows that our developed methods are more effective. Finally, we compare polynomigraphs of our developed methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method.
Read more

Reverse Zagreb and Reverse Hyper-Zagreb Indices for Silicon Carbide \(Si_{2}C_{3}I[r,s]\) and \(Si_{2}C_{3}II[r,s]\)

EASL-Vol. 1 (2018), Issue 2, pp. 37–50 | Open Access Full-Text PDF
Abaid ur Rehman Virk, Mirza Naveed Jhangeer, M. A. Rehman
Abstract:Topological indices collect information from the graph of molecule and help to predict properties of underlined molecule. Zagreb indices are among the most studied topological indices due to its applications in chemistry. In this report we compute first and second reversed Zagreb indices and first and second reversed Hyper Zagreb indices for \(Si_{2}C_{3}I[r,s]\) and \(Si_{2}C_{3}II[r,s]\). Moreover we also compute first and second reversed Zagreb polynomials and first and second reversed Hyper Zagreb polynomials for \(Si_{2}C_{3}I[r,s]\) and (Si_{2}C_{3}II[r,s]\).
Read more

Isolation, Purification and Complex Formation of Nicotine Alkaloid

EASL-Vol. 1 (2018), Issue 2, pp. 30–36 | Open Access Full-Text PDF
Sajid Mahmood, Saiqa Jameel, Zaheer Ahmad
Abstract:Nicotiana tabacum is rich with medicinal importance. The aim of the study is to isolate, purify and compare nicotine (3-[1-Methylpyrolidine-2 yl] pyridine) from different brands of cigarettes. Isolation is carried out by liquid-liquid extraction using ether as solvent. Crude nicotine samples are further purified with SPE (solid phase extraction) method. Nicotine crystals are complexed with zinc chloride (\(ZnCl_{2}\)). Fine and pure crystals of metal complexes are obtained with Nic-C and Nic-D. However, no complex formation is synthesized with Nic A and Nic-B due to impurities in the sample which is confirmed by thin layer chromatography. Antibacterial activity of the samples is carried out against different strains of bacteria which showed positive results for Nic-C and Nic-D. The outcomes of the study reveal that Zinc-Nicotine complexes can be used as therapeutic agents and anti-sickness agents in sickle cell disease.
Read more