A highly efficient and accurate numerical method for systems of fractional differential equations (FDEs) with rational order is presented in this paper. Rational power functions and rational Taylor series projection are utilized to obtain approximate solutions. Rational semi-smooth spaces are introduced, and the regularity of solutions in these spaces is established. A series of theoretical results, such as the existence and uniqueness of solutions, properties of the rational Taylor series and its remainder term, and an operational matrix approach, are derived. It is proven that the numerical solution is exact when the exact solution is a rational power series, and the approximate solution is shown to be the rational Taylor series projection of the exact solution. The convergence of the method is analyzed. The efficiency of the proposed method is demonstrated through numerical experiments, which show significant improvements in computational time compared to existing methods.

In the past few years, the area of mathematical study has made considerable advances, owing largely to the introduction of artificial intelligence (AI) tools. Among these, artificial neural networks (ANNs) have played an important role in modernizing several mathematical techniques and problem-solving approaches. ANNs have recently become popular as a powerful mathematical research tool, providing an effective alternative to established approaches for solving fractal-fractional differential equations (FFDEs). This paper describes the use of a feed-forward ANN with a hidden layer to address systems resulting from the fractal-fractional Bagley-Torvik differential equation (FFBTDE). In addition, a power series (PS) technique is introduced to increase efficiency. The paper looks at for solving FFBTDE with variable and constant coefficients. The numerical findings show that the suggested strategy not only produces results that closely match exact and reference solutions, but also outperforms existing methods in terms of accuracy.

In Saxon granulite mountains, significant deposits of hydrosiliceous nickel are characterized by their

relevant metal content, average metal concentrations, and thickness. The hydrosilicate deposits are Nirich

residue, formed by serpentinization process, due to the replacement process of nickel in the

immediate vicinity of serpentinites and nickel-bearing ore minerals (e.g., talc, chlorite nontronite,

cordierite, nepouite, other oxides and hydroxide magnesium minerals). X-ray and chemical analysis

indicate that the study area consists mainly of nickel, magnesium silicates, and hydrosilicate minerals,

with concentration of Ni varying from 2% to a few tens of ppm. A variety of lithological compositions

are present in these deposits, which are influenced by ultramafic rocks (serpentinite), talc and chloritic

clays, etc. The analysis of the mineralogical and geochemical composition of the Ni-ores also evidences

that the sources of Ni are ultramafic rocks derived from the mantle and concentration by

serpentinitization processes under discrete tectonic and metallogenic events. An important consideration

in the economics of these deposits is the mode of occurrence of nickel ores.

In this study, we numerically investigate two significant medical models, Ebola Viral Disease (EVD) and Blood Ethanol Concentration (BEC) models-both formulated using Caputo-fractional derivatives. We develop and apply the Modified Fractional Euler Method (MFEM) for their solution, with a specific focus on error analysis. Comparative studies with the classical Runge-Kutta fourth-order method (RK4M) demonstrate that MFEM provides a computationally efficient and accurate alternative for solving such systems. The major features of the given procedure are its ease of application to this type of problem and other systems in various fields, in addition to the absence of numerical errors accumulating. Finally, we can control the increase in the convergence rate and the stability of the simulation process. The convergence examination and error estimation for the suggested scheme are also included. The importance of this study also lies in its contribution to our understanding of the dynamics of these two models in their fractional form. In addition, those numerical investigations demonstrate how control parameters affect specific components within these models.

Background In arid regions such as Jennawen, Libya, groundwater is the primary source for drinking and irrigation, yet it is highly vulnerable to geogenic and anthropogenic contamination. This study aimed to assess the chemical and microbiological quality of 26 groundwater samples from rural and remote, including desalinated water. Material and Methods Physico-chemical parameters (e.g. pH, salinity, major ions) and microbiological indicators (total coliforms, E. coli, total bacterial counts) were analyzed according to established standards. Results revealed that most untreated groundwater samples exceeded the permissible limits for salinity, hardness, and sulfate. Furthermore, microbial bacterial contamination was found at various locations. While some RO desalinated water was free from microbiological contaminants, it was severely deficient in essential minerals. Conclusion The groundwater in the investigated area requires proper attention. Research and management strategies are critically needed to address both chemical and microbial contamination while maintaining an optimal mineral balance in potable water.

Abstract:

The Jabal Fezzan's xenolith has been intruded during Pan-African metamorphism, characterized by (high pressure and medium temperature), this process results in the formation of the biotite, muscovite, and kyanite metamorphic zones. There is a slight increase in the degree of metamorphism as it reaches the biotite zone. It consists of foliated, medium- to coarse-grained schists, mostly biotite, muscovite, and kyanite, additionally plagioclase and quartz, as well as zircon, rutile, and Fe oxides. The microscopical evidence indicates that iron-rich biotite in pelitic schists undergoes a series of chemical reactions that cause it to be formed and transformed into other minerals. P-T diagrams suggest that rocks in the study area might have been formed during collisions and decompressions of thickened continental crust. They are derived from sedimentary rocks such as greywacke, which contain high levels of Si4+ and Al3+. As P-T conditions pass through, the biotite isograd and biotite forms. This study highlighted the oldest metamorphic rocks in southern Libya, enhancing the understanding of the mantle source protolith metasomatism, and reducing the information gap between petrochemical significance and the evolutionary stage of Pan-African metamorphism in southern Libya through study xenolith outcrops in more detail.

 We give the approximate solution of the Riccati/Logistic differential equations (RDE/LDE). The suggested approach depends on the homotopy perturbation method developed with the Chebyshev series (CHPM). A study of the convergence analysis of CHPM is presented. The residual error function is calculated and used as a basic criterion in evaluating the accuracy and efficiency of the given numerical technique. We use the exact solution and the Runge-Kutta method of fourth order for comparison with the results of the method used. Through these results, we can confirm that the applied method is an easy and effective tool for the numerical simulation of such models. Illustrative models are given to confirm the validity and usefulness of the proposed procedure. 

In Mobile Ad Hoc Network (MANET) the applications of a multimedia system like video, audio broadcasting needs the path at which the data transmit might be reliable, delay-sensitive, and energy-efficient one. In addition, the delivery of information in vehicular networks (VANETs) is regarded as a demanding one because of high mobility and invariable topological difference. An existing routing protocol of ad hoc network fail to function better in terms of QoS metrics like packet delivery ratio (PDR), delay and so on., where there are heavy traffic and high mobility. So as to overcome the existing drawbacks, the proposed technique is implemented. In the proposed mechanism, the system model is initialized, and the route discovery process is carried by sending a route request. The multipath decision making (MPDM) scheme is employed to ensure the best route availability and the probability of link failure. Once the multipath decision-making condition is satisfied, the route path is established, and the communication takes place based on QoS constraint. Fuzzy based link monitoring scheme is employed to check the probability of link failure. Finally, the performance analysis is carried, and the comparison is made for proposed and existing mechanisms to prove the efficiency of the proposed scheme.

Abstract:

Tobacco is one of the sources that may introduce several heavy metals into the bodies of positive and negative smokers, leading to harmful effects on smokers’ bodies. Because a major number of Libyan populations are smoking different brands of cigarettes alongside raw tobacco leaves which may affect our citizens’ health, accordingly 10 cigarette brands comprising Bon International, Gold Mexico Original, Camel Yellow, D&G, Milano London, Milano, Oris Fliter. Karelia Ligts, Yes and Libyan brand named Ryadi, and another sample of raw tobacco leaves (LRT) planted locally were collected randomly from local shops distributed in Alassaba municipality with aims to determine the total concentration of Cadmium (Cd), Cobalt (Co), Copper (Cu), Lead (Pb) and Zinc (Zn) and calculate the health risk related to the presence of these metals in the most consumed tobacco. The obtained results showed that all collected tobacco samples contained various levels of Cd, Co, Cu Pb and Zn (mg/kg) ranged from 0.38 ± 0.07 to 0.84 ± 0.01, 0.33 ± 0.04 to 0.5 ± 0.07, 15.29 ± 0.88 to 18.75 ± 0.72, 0.42 ± 0.04 to 1.04 ± 0.11 and 14.33 ± 0.33 to 32.45 ± 2.09, respectively. The mean levels of Co, Cu and Zn were within the allowable levels set by the World Health Organization (WHO), whereas Pb and Cd levels were above the acceptable levels. The calculated harm quotient (HQ) of target metals were greater than 1 representing extreme health risk due to the presence of Cd, Cu Pb and Zn in studied tobacco, nevertheless, the HQ of Co were lower than 1 presenting minimal health risk to the smokers. In conclusion, there is a need to emphasize the regulation of the import and tread of tobacco and monitor the content of heavy metals in tobacco to reduce the health effects of these cigarette brands.    

Keywords: Cigarette brands, Heavy metals, Health risk, Smoking, Tobacco.

The current study aimed to the production and partial purification of a cold-active lipase by som fungi isolated from the olive oil processing wastes in Al-Gabal Al-Gharby, Libya. 31 fungal species from 12 genera were isolated. F. solani was the most prevalent comprising 94% of total Fusarium and 28.7% of total fungi, 102 fungal isolates were tested for their lipolytic activity on lipase production agar medium at 10 and 20°C. The most active isolates were Alternaria (2 isolates), Fusarium, and Penicillium (1isolate for each one). Molecular identification of the most active four isolates was carried out by their sequencing (ITS). The four powerful fungal strains' production of cold-active lipase was maximized by optimizing some nutritional and environmental factors. F. solani AUMC 16063 was able to produce the maximum amount of lipase activity (46.66U/mL/min) with specific activity (202.8U/mg), utilizing ammonium sulphate as a nitrogen source after 8 days of incubation at pH 3.0 and 15°C. However, at same condition after 6 days when yeast extract was employed as a nitrogen source, the generated cold-active lipase displayed the highest specific activity of (1550U/mg) and lipase activity (36.74U/ml/min). This is the first study in which the production, partial purification, maximized and characterization of a cold-active lipase enzyme by Fusarium solani. Keywords: cold active enzymes, Lipase, Fusarium solani, lipolytic activity, specific activity.