The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

Abstract

The use of modern scientific methods and techniques, is considered important topics to solve many of the problems which face some sector, including industrial, service and health. The researcher always intends to use modern methods characterized by accuracy, clarity and speed to reach the optimal solution and be easy at the same time in terms of understanding and application.

the research presented this comparison between the two methods of solution for linear fractional programming models which are linear transformation for Charnas & Cooper , and denominator function restriction method through applied on the oil heaters and gas cookers plant , where the show after reac

In this work, we first construct Hermite wavelets on the interval [0,1) with it’s product, Operational matrix of integration 2^k M×2^k M is derived, and used it for solving nonlinear Variational problems with reduced it to a system of algebric equations and aid of direct method. Finally, some examples are given to illustrate the efficiency and performance of presented method.

Nanoparticle has pulled in expanding consideration with the developing enthusiasm for nanotechnology which hold potential as essential segments for development applications. In the present work, a copper nanoparticle is manufactured as a suspension in distilled water by beating a bulk copper target with laser source (532 nm wavelength, 10 ns pulse duration and 10 Hz repletion rate) via method. UV- visible absorption spectra and AFM analysis has been done to observe the effect of repetition rate for the pulsation of laser. Copper nanoparticles (Cu-NPs) were successfully synthesized with green color. The Cu- NPs have very high purity because the preparation was managed in aqueous media to eliminate ambient contaminations.  Absorption

Graphite nanoparticles were successfully synthesized using mixture of H2O2/NH4OH with three steps of oxidation. The process of oxidations were analysis by XRD and optics microscopic images which shows clear change in particle size of graphite after every steps of oxidation. The method depend on treatments the graphite with H2O2 in two steps than complete the last steps by reacting with H2O2/NH4OH with equal quantities. The process did not reduces the several sheets for graphite but dispersion the aggregates of multi-sheets carbon when removed the Van Der Waals forces through the oxidation process.

The corrosion behavior of bare and chemical conversion coated (through anodizing) aluminum ASA 606 I in stagnant chromic acid solutions . Solutions of 2, 6 & J O wt. % Cr03 at 45°C, have been investigated using polarization technique. The anodizing experiments were conducted under fixed conditions of 35 minute exposure time and 30 volt supplied voltage. The most important feature achieved was the great difference in behavior between the anodic polarization curves for bare and anodized aluminum in different concentrations of chromic acid solutions.

This study involved preparation of Graphene oxide (GO) and reduced graphene oxide (RGO) using Hummer method and chemical method respectively. These carbon nanomaterials were used as starting material to make novel functionalize with thiocarbohydrazide (TCH) which was prepared by reacting CS2 with hydrazine to form GO or RGO- 4-amino,5-substituted 1H,1,2,4 Triazole 5(4H) thion (ASTT) ,(GOT) and( RGOT) respectively via cyclocondensation reaction. Also MnO2 nanorod was prepared to form hybridized with GOT and RGOT. A commercial multiwall carbon nanotube (MWCNT) and functionalization with carboxylic groups' (f-MWCNT) and its nanocomposite with GOT were also prepared. All carbon nanomaterials were characterized with different techniques such as

The performance of a batch undivided electrochemical reactor with a rotating cylinder electrode of woven-wire (60 mesh size), stainless steel 316, is examined for the removal of copper from synthetic solution of o.5 M sodium chloride containing 125 ppm at pH ≈ 3.5. The effect of total applied current, rotation speed on the figures of merit of the reactor is analyzed. For an applied current of 300 mA at 100 rpm, the copper concentration decreased from 125 to  mg l^-1 after 60 min of electrolysis with a specific energy consumption of 1.75 kWh kg^-1 and a normalized space velocity of 1.62 h^-1. The change in concentration was higher when the total applied currents were increased because of the turbulence

Atomic Force Microscope is an efficient tool to study the topography of precipitate. A study using Continuous Flow Injection via the use of Ayah 6SX1-T-2D Solar cell CFI Analyser . It was found that Cyproheptadine –HCl form precipitates of different quality using a precipitating agent's potassium hexacyanoferrate (III) and sodium nitroprusside. The formed precipitates are collected as they are formed in the usual sequence of forming the precipitate via the continuous flow .The precipitates are collected and dried under normal atmospheric pressure. The precipitates are subjected to atomic force microscope scanning to study the variation and differences of these precipitates relating them to the kind of response to both precipitates give