This article introduces a novel procedure to detect an approximate solution to Fredholm fractional integro-differential equations with linear type (LFFIDE) defined using Caputo fractional derivative. The new procedure approximates the solution using three types of polynomials: Laguerre polynomials, Hermite polynomials, and Legendre polynomials, thereafter transforming the problem into a linear programming problem. The approximate solutions are compared using testing examples to examine the efficiency of the suggested approach. Also, a comparison with the other methods using the same polynomials illustrates The effectiveness and consistency of the proposed technique. Finally, the error analysis of the proposed technique and convergent are discussed in the numerical test examples.
Abstract
An experimental study was conducted for measuring the quality of surface finishing roughness using magnetic abrasive finishing technique (MAF) on brass plate which is very difficult to be polish by a conventional machining process where the cost is high and much more susceptible to surface damage as compared to other materials. Four operation parameters were studied, the gap between the work piece and the electromagnetic inductor, the current that generate the flux, the rotational Spindale speed and amount of abrasive powder size considering constant linear feed movement between machine head and workpiece. Adaptive Neuro fuzzy inference system (ANFIS) was implemented for evaluation of a serie
... Show MoreA new four series of 2,2′-([1,1′- phenyl or biphenyl]-4,4′-diylbis(azanediyl)) bis(N′-((E)-1-(4-alkoxyphenyl) ethylidene) acetohydrazide) [V-XI]a,b and 1,1′-(2,2′-([1,1′- phenyl or biphenyl]-4,4′-diyl bis(azanediyl)) bis- (acetyl)) bis(3-(4-ethoxyphenyl)-1H-pyrazole-4-carbalde hyde) [XII-XVIII]a,b have been synthesized by varying terminal lateral alkoxy chain length (n = 1–3, 5–8), central linkage group (phenyl or biphenyl) and induced pyrazole heterocyclic ring in the main chain. The last two series were synthesized by the cyclization of substituted acetophenone hydrazones with Vilsmeier–Haack reagent (DMF/POCl3) to produce 4-formylpyrazole derivatives. The chemical structures of the synthesized compounds were examine
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The Non - Homogeneous Poisson process is considered as one of the statistical subjects which had an importance in other sciences and a large application in different areas as waiting raws and rectifiable systems method , computer and communication systems and the theory of reliability and many other, also it used in modeling the phenomenon that occurred by unfixed way over time (all events that changed by time).
This research deals with some of the basic concepts that are related to the Non - Homogeneous Poisson process , This research carried out two models of the Non - Homogeneous Poisson process which are the power law model , and Musa –okumto , to estimate th
... Show Morein this work the polymides were prepared as rthemally stable polymers by diffrent ways
Background: This review aims to discuss various canine retraction techniques using frictionless mechanics. Methods: Between 1930 and February 2022, searches were conducted about various canine retraction techniques using fixed orthodontic appliances in various databases, including PubMed Central, Science Direct, Wiley Online Library, the Cochrane Library, Textbooks, Google Scholar, Research Gate, and manual searching. Results: After removing the duplicate articles, publications that described how to use archwires to perform canine retraction with the archwires were included. Conclusions: The pros and cons of various canine retraction techniques using archwires were thoroughly discussed. T-loop is the preferred spring of all because of it
... Show MoreDuring the last decade, there has been a concern about the relation between aluminum residuals in treated water and Alzheimer disease, and more interest has been considered on the development of natural coagulants. The present study aimed to investigate the efficiency of alum as a primary coagulant in conjunction with mallow, Arabic gum and okra as coagulant aids for the treatment of water samples containing synthetic turbidity of kaolin. Jar test experiments were carried out for initial raw water turbidities 100, 200 and 500 (NTU). The optimum doses of alum, mallow, Arabic gum and okra were 20, 2, 1 and 1 mg/L for100 NTU turbidity level, 35, 4, 2 and 3 mg/L , for 200NTU turbidity level and 50, 8, 10 and 8 mg/L for 500 NTU turbidity leve
... Show MoreThis research aims to investigate the thermal performance of different thermal composite insulators, wrapped around a closed-loop copper pipe (CLP). To achieve this aim a system was designed and manufactured. It is consisted of closed water tank insulated by Rock Wool, and supplied with two electric heaters, two thermostat, a flow meter, a water pump, digital temperature scales, and four series of (CLP).
Six insulators were prepared namely; composites of Impregnated Fiberglass with Elastoclad and foaming Rubber (FER), Impregnated Fiberglass with Elastoclad resin and Polymeric Membrane (FEM), Impregnated Fiberglass with Polyurethane thermoset resin and Foaming Rubber (FUR), Impregnated Fiberglass with Polyurethane thermoset resin and P