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

Background: Congenital heart disease is one of the most common developmental anomalies in children. These patients commonly have poor oral health that increase caries risk. Dental management of children with congenital heart disease requires special attention, because of their heightened susceptibility to infectious endocarditis. The aims of this study were to assess the severity of dental caries of primary and permanent teeth and treatment needs in relation to nutritional indicator (Body Mass Index) among children with congenital heart disease. Materials and Methods: In this case-control study, case group consisted of 399 patients aged between 6-12 years old with congenital heart disease were examined for dental status in Ibn Al-Bitar spec

Burn is one of the most devastating traumas that someone can encounter in their life. Burn wound sepsis is still the leading cause of death in burned patients. Appropriate knowledge of the causative pathogen in burn sepsis is important for successful patient management and for the reduction of the incidence of antibiotic resistance. A retrospective study was conducted between 2010 and 2018 at the Burn Specialty Hospital in Baghdad.Atotal of 320 blood culture samples were obtained from patients with sepsis orsuspected of having sepsis. Patient age ranged between 9 months to 70 years old, with a mean total burn surface area of 45.26%. The most common microorganisms isolated from those patients who had sepsis or suspicion of sepsis were Klebsi

Background: In type 2 diabetes mellitus there is a progressive loss of beta cell function. One new
approach yielding promising results is the use of the orally active dipeptidyl peptidase-4 (DPP-4)
inhibitors for type 2 diabetes mellitus.
Objective: This study aims at comparing the possible occurrence of macrovascular & microvascular
complications in Iraqis patients with type 2 diabetes mellitus using two combinations of drugs
metformin + glibenclamide and metformin + sitagliptin.
Methodology: Sixty eight T2DM patients and 34 normal healthy individuals as control group were
enrolled in this study and categorized in to two treatment groups. The group 1 (34 patients ) received
metformin 500 mg three times daily

The significance of the work is to introduce the new class of open sets, which is said Ǥ- -open set with some of properties. Then clarify how to calculate the boundary area for these sets using the upper and lower approximation and obtain the best accuracy.

Some Results on Fuzzy Zariski

Topology  on Spec(J.L)

     The aim of this paper is to study the nonlinear delay second order eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the least square method which will be developed to solve this kind of problems.