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Novel Definitions of α-Fractional Integral and Derivative of the Functions

     An α-fractional integral and derivative of real function have been introduced in new definitions and then, they compared with the existing definitions. According to the properties of these definitions, the formulas demonstrate that they are most significant and suitable in fractional integrals and derivatives. The definitions of α-fractional derivative and integral coincide with the existing definitions for the polynomials for 0 ≤ α < 1. Furthermore, if α = 1, the proposed definitions and the usual definition of integer derivative and integral are identical. Some of the properties of the new definitions are discussed and proved, as well, we have introduced some applications in the α- fractional derivatives and integrals. Moreover, α-power series and α–rule of integration by parts have been proposed and implemented in this study. 

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Publication Date
Wed Dec 25 2019
Journal Name
International Journal Of Corrosion And Scale Inhibition
Evaluation and characterization of the symbiotic effect of benzylidene derivative with titanium dioxide nanoparticles on the inhibition of the chemical corrosion of mild steel

A new benzylidene derivative, namely N-benzylidene-5-phenyl-1,3,4-thiadiazol-2-amine (BPTA), has been synthesized and instrumentally confirmed with Elemental Analysis (CHN), Nuclear Magnetic Resonance (NMR), and Fourier Transform Infrared Spectroscopy (FT-IR). Titanium Dioxide (TiO2) nanoparticles (NPs) were synthesized and characterized by X-ray. The mutualistic complementary dependence of BPTA with TiO2 nanoparticles as anti-corrosive inhibitor on mild steel (MS) in 1.0 M hydrochloric acid has been tested at various concentrations and various temperatures. The methodological work was achieved by gravimetric measurement methods complemented with surface analysis. The synthesized inhibitor concentrations were 0.1 mM to 0.5 mM and the temper

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Scopus (62)
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Publication Date
Sun Sep 07 2014
Journal Name
Baghdad Science Journal
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Publication Date
Tue Jan 01 2019
Journal Name
J. Mech. Cont.& Math. Scis
Publication Date
Sat Mar 11 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
On the Degree of Best Approximation of Unbounded Functions by Algebraic Polynomial

  In this paper we introduce a new class of degree of best algebraic approximation polynomial Α,, for unbounded functions in weighted space Lp,α(X), 1 ∞ .We shall prove direct and converse theorems for best algebraic approximation in terms modulus of smoothness in weighted space

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Publication Date
Wed Mar 25 2015
Journal Name
Comptes Rendus Chimie
A novel method for the synthesis of biodiesel from soybean oil and urea

The increasing demand for energy has encouraged the development of renewable resources and environmentally benign fuel such as biodiesel. In this study, ethyl fatty esters (EFEs), a major component of biodiesel fuel, were synthesized from soybean oil using sodium ethoxide as a catalyst. By-products were glycerol and difatty acyl urea (DFAU), which has biological characteristics, as antibiotics and antifungal medications. Both EFEs and DFAU have been characterized using Fourier transform infrared (FTIR) spectroscopy, and 1H nuclear magnetic resonance (NMR) technique. The optimum conditions were studied as a function of reaction time, reactant molar ratios, catalyst percentage and the effect of organic solvents. The conversion ratio of soybea

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Scopus (10)
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Publication Date
Sat Jan 01 2022
Journal Name
Technologies And Materials For Renewable Energy, Environment And Sustainability: Tmrees21gr
The effect of plasma jet-generated gold nanoparticles on liver functions

In this study, gold nanoparticles (AuNPs) were synthesized using a plasma jet system at different exposure times. Using ultraviolet, visible spectra, X-ray diffraction, the nanoparticles were characterized (XRD). A Plasmon surface resonance concentrated at 530, 540, and 533 nm for the prepared AuNPs. The pattern of XRD showed that the extreme peaks of the film reflect crystalline existence. The face-centered cubic structure of the gold nanoparticles was prepared for all samples, with an average crystallite size of 25-40 nm. The effect of AuNPs in vivo on liver function levels was measured. For all doses, we notice an increase in the ranks of liver function in the blood during the period of dosing, and it begins to decrease when the dosi

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Publication Date
Mon Mar 08 2021
Journal Name
Baghdad Science Journal
Evaluation of the one electron expeetation values for different wave functions

The aim of this work is to evaluate the onc-electron expectation values < r > from the radial electronic density funetion D(r) for different wave ?'unctions for the 2s state of Li atom. The wave functions used were published in 1963,174? and 1993 , respectavily. Using " " ' wave function as a Slater determinant has used the positioning technique for the analysis open shell system of Li (Is2 2s) State.

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Publication Date
Sun Mar 12 2017
Journal Name
Al-academy
Functions of Repetition in Deeping the Esthetic Meaning in Television Drama

The audio-visual arts are considered modern arts compared to theater, plastic arts, and music. It proved its distinguished presences among other arts. It was capable of forming a huge audience and took television from cinema, literature, theater, type of narration, and narrative instructor. Also, it took symbolism and metaphorical repetition from literature. As for the importance of the functions that repetition has the research concentrated on the importance of function of repetition in deeping the esthetic meaning in television drama. The research was limited by:1.Objective limit: functions of repetition in deeping the esthetic meaning in series of (Harem Al-Sultan).2.Place where it was showed: series of (Harem Al-Sultan) part four on

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Publication Date
Thu Jan 24 2019
Journal Name
Journal Of Education College Wasit University
Postmodernism and Technology in Don Delillo's Novel The White Noise

This paper aims at investigating the effect of postmodernism and technology on the social life in Don Delillo's novel The White Noise. In this novel, Don Delillo portrays the chaotic life by using modern technology which has been presented by three ways. The first way is by television as being a source of information and entertainment. The second way is by the toxic event whereas the third is by Dylar's episode and its destructive consequences. He depicts that through the atmosphere of Jack's family plus its effects on the life and thoughts of the elders and society. He proves that technology is leading humanity not to safety, but to death. He further highlights that by showing the impact of technology on the life of the main charac

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Publication Date
Thu Jun 18 2020
Journal Name
Biochem. Cell. Arch.
NEW DERIVATIVE OF CHITOSAN BASED ON EPICHLOROHYDRNE, SYNTHESIS, CHARACTERIZATION, ANTIBACTERIAL ACTIVITY AND SWELLING STUDY

A novel series of chitosan derivatives were synthesized via reaction of chitosan with carbonyl compounds and grafted it’s by with different amine compounds substituted hydrogen. The produced polymers were characterized by different analyses FTIR, 1HCNMR, XRD, DSC and TGA. Solubility in water as well as many solvent was investigated, antibacterial activity of chitosan and its derivatives against two types of bacteria E. coli and S. aureus was also investigated. The results showed that derivatives sort of have antibacterial activities against Esherichia coli (Gram negative) better than chitosan whilst compound IX has better antibacterial against Staphylococcus aureus (Gram positive). SEM analysis showed that increase of surface roughness wi

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