In this paper, we present a new non-convex hybrid iteration algorithm for common fixed points of a uniformly closed asymptotically family of countable quasi-Lipschitz mappings in the domains of Hilbert spaces.

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].

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.

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.

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.

In this paper, we study Katugampola fractional differential equations (FDEs) with nonlocal conditions on time scales. By means of standard fixed point theorems, some new sufficient conditions for the existence of solutions are established.

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.

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.

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.

Nanoparticles are nanosized clusters with dimensions less than 100nm. Nanoparticles are fabricated by physical, chemical, and biological methods. Physical and chemical methods are energy intensive and involve hazards of contaminations. Biological synthesis of nanoparticles is environment friendly, less toxic and cost effective process. Plants, microorganisms, and biomolecules are commonly exploited species for merging of nanoparticles in this method. In present work we synthesize Chromium oxide nanoparticles by biological method using fungal extract of Aspargillus Niger. The synthesized nanoparticles are characterized by XRD (X-Ray Diffraction), SEM (Scanning Electron Microscopy) and UV-Vis (Ultraviolet Visible) techniques.