ABSTRACT: This paper applies the Abaoub – Shkheam Decomposition Method (QDM) to obtaining solutions of linear fractional diffusion equations. The fractional derivative is described in the Caputo sense. Some illustrative examples are given, revealing the effectiveness and convenience of the method. 

Abstract: In this paper, a nonlinear fractional diffusion and wave equations are solved using the Abaoub-Shkheam Decomposition Method (QDM). The Caputo sense is used to characterise the fractional derivative. An example is provided to demonstrate the method's efficiency and practicality.

This research documents the initial finding of Chloris pycnothrix Trin., frequently referred to as spiderweb chloris, in Libya, particularly from the Ariggiba region close to Sabha city. This grass, originating from tropical and subtropical regions, is versatile and may become invasive. It was recognized via morphological examination during field surveys in 2023–2024, with samples stored in a herbarium. The species flourishes in alluvial plains as well as in disturbed habitats like road shoulders. It can be mistaken for Chloris virgata, although they differ in some important morphological aspects. It was previously believed that only one species of Chloris existed in Libya. This study provides a revision and an identification key for them in the context of Libyan flora. The tolerant nature of C. pycnothrix to drought, combined with its ability to colonize poorly maintained land, makes its potential introduction—most likely through anthropogenic means—alarming ecologically and emphasizes the need for management strategies to contain its spread and monitor its impact. 

Abstract: The Abaoub-Shkheam Decomposition Method (QDM) is employed in this paper to solve nonlinear initial value problems of second order. Adomian polynomial is used to decompose nonlinear functions that exist in a given equation. We are using this method (QDM) to find the exact solution of different types of non-linear ordinary differential equations, which is based on the Abaoub Shkheam transform method (QTM) and the Adomian Decomposition Method (ADM). An example is provided to demonstrate the efficacy of this approach. 

Coronary artery disease (CAD) is the leading cause of death worldwide. the study aims to evaluate the association between plasma lipoprotein-associated phospholipase A2 (Lp-PLA2) and Libyan individuals' clinical and biochemical risk factors for CAD. This cross-sectional study assessed plasma concentration of Lp-PLA2 between patients with CAD and those without CAD in both genders based on clinical history, exercise ECG, two-dimensional echocardiography, and coronary angiography. Several biochemical parameters were estimated. Plasma levels of Lp-PLA2 were measured. 181 individuals were recruited for this study, including 125 with CAD and 56 without CAD. Plasma Lp-PLA2 concentration was significantly higher in patients with CAD versus individuals without coronary artery disease. In addition, the plasma concentration of Lp-PLA2 was higher in patients >60 years of age compared with patients <60 years old. To conclude Plasma level of Lp-PLA2 concentration was independently correlated with CAD, an inflammatory marker such as high sensitivity C-reactive protein among Libyan patients.

In the current study a new family of distributions called the odd Lindley Log compound Rayleigh distribution is introduced and studied. Some statistical properties of the new distribution including moments, moment generating function and Renyi entropy are derived. Parameter estimations are obtained via the maximum likelihood method and the observed information matrix is derived. Finally, a real dataset is used to illustrate the importance and flexibility of the new proposed distribution.

Keywords—Odd Lindley, Rayleigh, Distribution, Entropy

Abstract: The Study aims to evaluate the quality of groundwater in the Ain Zara area, situated south of Tripoli, and assesses its suitability for drinking using the Canadian Water Quality Index (CCMEWQI) and the Weighted Arithmetic Index (WAWQI). A total of 40 well water samples were collected in March and April 2023, with GPS data collected for the wells and mapped accordingly. Key parameters measured included dissolved oxygen (DO), nitrite (NO2-), electrical conductivity (EC), total dissolved salts (TDS), pH, and concentrations of positive ions (Ca²⁺, Na⁺, K⁺, Mg²⁺) as well as negative ions (NO3-, SO4²-, Cl-, HCO3-). Chemical Oxygen Demand (COD) and Biological Oxygen Demand (BOD) were calculated, with results compared against the Libyan Standard Specifications for Drinking Water No. 82 (2013). Analysis indicated an increase in TDS concentration in select samples, exceeding the maximum concentration (7100 mg/L) in well 10, alongside elevated sodium ion concentrations in wells (10, 11, 12, 13, 14, 16, 17, 18, 19, 32, 34, 35, 36, 37) and calcium ions in wells (7, 10, 13, 14, 15, 16, 17, 18, 32) and 35 in the northern and northwestern sections of the study area. Furthermore, increased concentrations of chloride and bicarbonate ions were observed in the wells to the north and northwest. Other parameters remained within the permissible limits according to the 2013 Libyan standard specifications. Wells (1, 2, 3, 6, 9, 21, 22, 23, 25, 26, 27, 28, 31, 38, 39, and 40), located in the southern and southeastern parts of the study area, were classified as excellent quality for drinking, according to both the CCMEWQI and WAWQI. In contrast, the remaining wells in the northern and northwestern areas were classified from good to acceptable to poor, rendering them unsuitable for drinking. The study demonstrated that both indices displayed similar spatial distributions.

Professor Salem Aboglila                                                           

Geochemistry & Environmental Chemistry science Faculty – Azzaytuna University-Libya

Mobile : 00218913700361

            :00218923394183

Email: salem.aboglila@gmail.com 

Address: Salem Abdul Ghni Aboglila / TIP 52945, Aramex House Old Bath Road Colnbrook, Slough,Berkshire SL3 0NS 

Nov 2010 PhD degree Thesis title: Organic and Isotopic Geochemistry of Source-rocks and Crude Oils from the East Sirte Basin (Libya). Curtin University of technology (palaeoenvironment study)

For the first time in Libyan flora, a new record for Boerhavia repens L is recorded. This widespread wild weed was collected from the Ariggiba region (110 km west-south Sabha city). A full description, habitat information, distribution map, and distribution data are provided to facilitate further identification and future detection. A brief discussion about the most important threats this species poses is presented.

Shhoob Mahammed imhmed Elahmir, Khaleefah Salem Imohammed, (11-2024), Scientific Reports in Life Sciences: Scientific Reports in Life Sciences, 4 (5), 59-66

Abstract: In this study, we introduce a novel approach to the solution of a nonlinear Volterra -Fredholm integral equations by applying the Adomian decomposition method under the effect of the Abaoub- Shkheam transform. We demonstrate the existence and uniqueness of the solution in Banach space and illustrate this idea with an example.