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

Stainless steel (AISI 304) has good electrical and thermal conductivities, good corrosion resistance at ambient temperature, apart from these it is cheap and abundantly available; but has good mechanical properties such as hardness. To improve the  hardness and corrosion resistance of stainless steel its surface can be modified by developing nanocomposite coatings applied on its surface. The main objective of this paper is to study effect of electroco-deposition method on microhardness and corrosion resistance of stainless steel, and to analyze effect of nanoparticles (Al₂O₃, ZrO₂ , and SiC)  on properties of composite coatings. I

In this research, the results of the Integral breadth method were used to analyze the X-ray lines to determine the crystallite size and lattice strain of the zirconium oxide nanoparticles and the value of the crystal size was equal to (8.2nm) and the lattice strain (0.001955), and then the results were compared with three other methods, which are the Scherer and Scherer dynamical diffraction theory and two formulas of the Scherer and Wilson method.the results were as followsScherer crystallite size(7.4nm)and lattice strain(0.011968),Schererdynamic method crystallite size(7.5 nm),Scherrer and Wilson methodcrystallite size( 8.5nm) and lattice strain( 0.001919).And using another formula for Schearer and Wilson methodwe obtain the size of the c

In this work, ZnO quantum dots (Q.dots) and nanorods were prepared. ZnO quantum dots were prepared by self-assembly method of zinc acetate solution with KOH solution, while ZnO nanorods were prepared by hydrothermal method of zinc nitrate hexahydrate Zn (NO3)2.6H2O with hexamethy lenetetramin (HMT) C6H12N4. The optical , structural and spectroscopic properties of the product quantum dot were studied. The results show the dependence of the optical properties on the crystal dimension and the formation of the trap states in the energy band gap. The deep levels emission was studied for n-ZnO and p-ZnO. The preparation ZnO nanorods show semiconductor behavior of p-type, which is a difficult process by doping because native defects.

Electrocoagulation is an electrochemical method for treatment of different types of wastewater  whereby sacrificial anodes corrode to release active coagulant (usually aluminium or iron cations) into solution, while simultaneous evolution of hydrogen at the cathode allows for pollutant removal by flotation or settling. The Taguchi method was applied as an experimental design and to determine the best conditions for chromium (VI) removal from wastewater. Various parameters in a batch stirred tank by iron metal electrodes: pH, initial chromium concentration, current density, distance between electrodes and KCl concentration were investigated, and the results have been analyzed using signal-to-noise (S/N) ratio. It was found that the r

An application of neural network technique was introduced in modeling the point efficiency of sieve tray, based on a
data bank of around 33l data points collected from the open literature.Two models proposed,using back-propagation
algorithm, the first model network consists: volumetric liquid flow rate (QL), F foctor for gas (FS), liquid density (pL),
gas density (pg), liquid viscosity (pL), gas viscosity (pg), hole diameter (dH), weir height (hw), pressure (P) and surface
tension between liquid phase and gas phase (o). In the second network, there are six parameters as dimensionless
group: Flowfactor (F), Reynolds number for liquid (ReL), Reynolds number for gas through hole (Reg), ratio of weir
height to hole diqmeter