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.

The negotiation phase is gaining great importance in investment loans due to the magnitude of the amounts awarded and the need to obtain adequate lending guarantees and the development of better conditions, and this requires that negotiating policy with fixed principles that balance between meeting the demands of customers and maintain market share and achieve profits and avoid defaults and losses the bank, and so I have touched Find the concept of investment loans and procedures for granting and the concept of the negotiation process for the granting of loans. The practical side to ensure the preparation of examination form consists of questions commensurate with the methodology developed by the researchers, were directed to the officia

      The combined system of electrocoagulation (EC) and electro-oxidation (EO) is one of the most promising methods in dye removal. In this work, a solution of 200 mg/l of Congo red was used to examine the removal of anionic dye using an EC-EO system with three stainless steel electrodes as the auxiliary electrodes and an aluminum electrode as anode for the EC process, Cu-Mn-Ni Nanocomposite as anode for the EO process. This composite oxide was simultaneously synthesized by anodic and cathodic deposition of Cu (NO3)2, MnCl2, and Ni (NO3)2 salts with 0.075 M as concentrations of each salt with a fixed molar ratio (1:1:1) at a constant current density of 25 mA/cm2. The characteristics structure and surface morphology of the depo

Combining different treatment strategies successively or simultaneously has become recommended to achieve high purification standards for the treated discharged water. The current work focused on combining electrocoagulation, ion-exchange, and ultrasonication treatment approaches for the simultaneous removal of copper, nickel, and zinc ions from water. The removal of the three studied ions was significantly enhanced by increasing the power density (4–10 mA/cm2) and NaCl salt concentration (0.5–1.5 g/L) at a natural solution pH. The simultaneous removal of these metal ions at 4 mA/cm2 and 1 g NaCl/L was highly improved by introducing 1 g/L of mordenite zeolite as an ion-exchanger. A remarkable removal of heavy metals was reported