This work describes two efficient and useful methods for solving fractional pantograph delay equations (FPDEs) with initial and boundary conditions. These two methods depend mainly on orthogonal polynomials, which are the method of the operational matrix of fractional derivative that depends on Bernstein polynomials and the operational matrix of the fractional derivative with Shifted Legendre polynomials. The basic procedure of this method is to convert the pantograph delay equation to a system of linear equations and by using, the operational matrices we get rid of the integration and differentiation operations, which makes solving the problem easier. The concept of Caputo has been used to describe fractional derivatives. Finally, some

Because the Coronavirus epidemic spread in Iraq, the COVID-19 epidemic of people quarantined due to infection is our application in this work. The numerical simulation methods used in this research are more suitable than other analytical and numerical methods because they solve random systems. Since the Covid-19 epidemic system has random variables coefficients, these methods are used. Suitable numerical simulation methods have been applied to solve the COVID-19 epidemic model in Iraq. The analytical results of the Variation iteration method (VIM) are executed to compare the results. One numerical method which is the Finite difference method (FD) has been used to solve the Coronavirus model and for comparison purposes. The numerical simulat

Most of the water pollutants with dyes are leftovers from industries, including textiles, wool and others. There are many ways to remove dyes such as sorption, oxidation, coagulation, filtration, and biodegradation, Chlorination, ozonation, chemical precipitation, adsorption, electrochemical processes, membrane approaches, and biological treatment are among the most widely used technologies for removing colors from wastewater. Dyes are divided into two types: natural dyes and synthetic dyes.

The charge transfer at C23H17F8N8O2PRu, C44H30BF4N5O4Ru, C56H52CL5N5OOsP2 and C76H88F80N24O11P10Ru4 nitrosyl complexes are investigation and studies theoretically using the quantum consideration. Charge transfer behavior largely rely to the electric properties of nitrosyl complexes system whose depending on the main important parameters for the transmission rate constant such that: orientation transition energy, overlapping coupling coefficient, driving force energy, height barrier and Temperature T (K). Data results have been evaluated using a MATLAB program. Results show that rate of charge transfer increases due to increases the orientation transition energy.

Cephalexin and its derivatives are commonly utilized in the pharmaceutical and medicinal industry due to their biological and pharmaceutical activities, including anti-microbial, anti-cancer, anti-bacterial, and herbicidal activities as well as possessing high palatability and being useful for skin and joint infections. Interestingly, some organic drugs, including cephalexin, which exhibit toxicological and pharmacological properties, can be administered in forms of metal complexes. Many researchers have synthesized organic ligands derived from cephalexin in forms of Schiff bases and azo compounds which exhibited higher biological and medicinal properties when compared to cephalexin alone. One of the important features that make Schiff base

Complexes of some metal ions with 2-thiotolylurea were prepared in ethanolic medium using (1:1) (Metal : Ligand) ratio yielded series of neutral complexes as the general formula [M(L)Cl2]. The prepared complexes were identified by atomic absorption FT.IR, UV-Visble spectra, molar conductivity and magnetic properties. From the above data the tetrahedral structure was suggested for all complexes.

Cerium (III), Neodymium (III) and Samarium (III) Complexes existent a wide range of implementation that stretch from their play in the medicinal and pharmaceutical area because of their major significant pharmacological characteristic such as antifungal, anti-cancer, anti-bacterial ,anti-human immunodeficiency virus ,antineoplastic, anti-inflammation,inhibition corrosion,in some industrial (polymers, Azo dye).It is likely to open avenuesto research among various disciplines such as physics, electronics, chemistry and materials science by these complexes that contain exquisitely designed organic molecules.This paper reviews the definition, importance and various applications of Cerium (III), Neodymium (III) and Samarium (III) Complexe