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.

APDBN Rashid, International Journal of Humanities and Social Sciences/ RIMAK, 2023

Background: Obesity is considered an important risk factor for periodontal disease. It has been reported that reactive oxygen species linking both diseases, systemic melatonin supplementation as antioxidant therapy, was addressed as an adjuvant to scaling and root surface debridement (SRP) to enhance the treatment of periodontitis. Objective: To investigate the efficacy of systemic melatonin administration in periodontitis-obese patients as an adjuvant to scaling and root surface debridement (SRP). Methods: A randomized clinical trial was conducted at a dental-specialized center. Eighty subjects were included and allocated into group-I: twenty periodontium-healthy, normal-weight people; group-II: 30 obese patients with stage-III tre

Axial spondyloarthritis (axSpA) is a chronic rheumatic inflammatory disease affecting mainly the spine and sacroiliac joints. Since the copper-to-zinc ratio (Cu/Zn) indicates an inflammatory response, the change in ratio is expected to correlate with axSpA. This study compared levels of Cu/Zn in the serum of axSpA patients. Serum samples were obtained from 53 patients with axSpA divided according to biological treatment into cohorts A and B, and 28 healthy control as cohort C. Serum levels of Cu and Zn were determined first by a fully automated chemistry analyzer TC-Matrix Plus, then the ratio was obtained. The elevated serum Cu concentration means of cohort B (189.32 ± 13.808 µg/dL) compared to cohort A (168.85 ± 7.244 µg/dL) a

This work is an experimental investigation for single basin-single slope solar still coupled with an evacuated tube solar collector. The work is carried out under the climatic conditions of Baghdad city (33.2456º North and East latitude, 44.3337º longitude) through certain days of the months of the year 2019 to study the impact of using evacuated tube solar collector on the daily productivity and efficiency under the outdoors climatic conditions. It was found that using the evacuated tube solar collector increase daily productivity from 2.175 kg/  to 2.95 kg/ for 9 hours (35.63 %) for clear days, also an enhancement about 10.97 % in daily efficiency.

A field experiment was conducted during the spring season 2020 in Karbala proving/ Al-Sharia Distrit, located at latitude N 32° 42' 13.8" and longitude E 43° 54' 36.6" and at an altitude of 27 m above sea level. The experiment included a study of two factors: the first, Irrigation Interval, three treatments were used: irrigation treatment every 2 days, Irrigation treatment every 4 days, and Irrigation treatment every 6 days. The second factor is the addition of soil conditioners, in which four treatments were used: the control treatment without any addition, the treatment of adding bio-organic fertilizers, the treatment of adding water-conserving technology (polymer), and the treatment of adding water-conserving technology + fertilizers O

Numerical study of separation control on symmetrical airfoil, four digits (NACA

0012) by using rotating cylinder with double steps on its upper surface based on the computation of Reynolds-average Navier- Stokes equations was carried out to find the optimum configuration of unconventional airfoil for best aerodynamics performance. A model based on collocated Finite Volume Method was developed to solve the governing equations on a body-fitted coordinate system. A revised (k-w) model was proposed as a known turbulence model. This model was adapted to simulate the control effects of rotating cylinder. Numerical solutions were performed for flow around unconventional airfoil with cylinder to main stream velocities ratio in the range

The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimi

This paper investigated the fatigue life behavior of two composite materials subjected to different times of shot peening (2, 4 and 6 min).The first material prepared from unsaturated polyester with E-glass reinforcement by 33% volume fraction. While, the second one was prepared from unsaturated polyester with aluminum powder by2.5% volume fraction. The experimental results showed that the improvement in endurance limit was obtained (for the first material) at 2, 4 and 6 min shot peening times where the percentage of maximum improvement was 25% at shot peening time of 6 min. While, the endurance limit of the second material decreased at shot peening times of 2, 4 and 6 min where the percentage of maximum reduction was 29 % at shot peenin