In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

This paper presents a comparative study between different oil production enhancement scenarios in the Saadi tight oil reservoir located in the Halfaya Iraqi oil field. The reservoir exhibits poor petrophysical characteristics, including medium pore size, low permeability (reaching zero in some areas), and high porosity of up to 25%. Previous stimulation techniques such as acid fracturing and matrix acidizing have yielded low oil production in this reservoir. Therefore, the feasibility of hydraulic fracturing stimulation and/or horizontal well drilling scenarios was assessed to increase the production rate. While horizontal drilling and hydraulic fracturing can improve well performance, they come with high costs, often accounting for up t

Background: Denture fracture is one of the most common problems encountered by the patients and prosthodontists. The objective of present study was to evaluate the transverse strength of nylon denture base resin repaired by using conventional heat polymerized, autopolymerized and visible light cure {VLC} resins, surface treatment that used for repair and adjustment of insufficient nylon denture bases and in case of addition of artificial teeth. As these corrective procedures are common chair side procedures in dental clinic. Materials and methods: One hundred twenty nylon specimens were prepared by using metal patterns with dimension of (65x10x2.5 mm) length, width, and thickness respectively for transverse strength test while for tensile b

Background: Polymethylmethacrylate (PMMA) has relatively unsatisfactory mechanical properties such as low flexural strength and impact strength also dimensional instability. Material and method: Zirconium silicate nanoparticles were coated with a layer of trimethoxysilylpropylmethacrylate (TMSPM) before sonication in monomer (MMA) with the percentages 1% and 1.5% by weight then mixed with powder using conventional procedure, (150) samples were prepared and divided into three groups, each group consisted of (50) samples, the first group prepared from PMMA without addition (control), another group with the addition of 1% wt Zrsio4 nanoparticles (experimental) and the third one with 1.5% wt Zrsio4 nanoparticles (experimental). Each group

Background: Polymethyl methacrylate (PMMA) is the most commonly used material in denture fabrication. The material is far from ideal in fulfilling the mechanical requirements. Midline fracture; poor thermal conductivity and water sorption, are common problem in this material. The purpose of this study was to evaluate the effect of addition of surface treated Aluminum oxide nano fillers on some properties of heat cured (PMMA). Materials and methods: In addition to controlled group of heat cured PMMA the silanized (Al2O3) nanoparticles was added to PMMA powder by weight in three different percentages 1wt%, 2wt% and 3wt%, mixed by probe ultra-sonication machine. 200 specimens were constructed and divided into 5 groups according to the test (e

Background: Heat-cured poly (methyl methacrylate) the principal material for the fabrication of denture base have a relatively poor mechanical properties. The aim of this study was to investigate the effect of glass flakes used as reinforcement on the surface hardness and surface roughness of the heat-processed acrylic resin material. Material and method: Glass flakes (product code: GF002) pretreated with silane coupling agent were added to Triplex® denture base powder using different concentrations. A total of 100 specimens of similar dimensions (65 x 10 x 2.5) mm were prepared, subdivided into 2 main groups of 50 specimens for each of the study tests. Ten specimens for the control group and 40 specimens for each of the experimental gro

Surface drip irrigation is one of the most conservative irrigation techniques that help control providing water directly on the soil through the emitters. It can supply fertilizer and providing water directly to plant roots by drippers. One of the essential needs for trickle irrigation nowadays is to obtain more knowledge about the moisture pattern under the trickling source for various types of soil with various discharge levels with trickle irrigation. Simulation numerical using HYDRUS-2D software, version 2.04 was used to estimate an equation for the wetted area from a single surface drip irrigation in unsaturated soil is taking into account water uptake by roots. In this paper, using two soil types were used, namely

In this work, 332 Al alloy was prepared and reinforced with (0.5% and 1%) nano-Al₂O₃ particles. The prepared unreinforced and reinforced 332 Al alloy with nano-Al₂O₃ were solution heat treated (T6) at 510 ̊C and aged at 225 ̊C with different times (1, 3, and 5 h). Hardness test was performed on all the prepared alloys. All prepared alloys were dry slided under different applied loads (5, 10, 15, and 20 N) against steel counterface surface using pin on disk apparatus. The results showed that refinement effect was observed after addition of nano-Al₂O₃ particles and a change in silicon morphology after performing the solution heat treatment. The results also showed that har

In this paper, we describe the cases of marriage and divorce in the city of Baghdad on both sides of Rusafa and Karkh, we collected the data in this research from the Supreme Judicial Council and used the cubic spline interpolation method to estimate the function that passing through given points as well as the extrapolation method which was applied for estimating the cases of marriage and divorce for the next year and comparison between Rusafa and Karkh by using the MATLAB program.