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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
Fri Mar 01 2019
Journal Name
Journal Of Global Pharma Technology
Simultaneous Determination of Furosemide, Carbamazepine, Diazepam and Carvedilol in Quaternary Mixture via Derivative Spectrophotometry

Quick and accurate quaternary mixture resolution of furosemide (FURO), carbamazepine (CARB), diazepam (DIAZ) and carvedilol (CARV) by using derivative spectrophotometric method was performed. FURO and CARV were determined by means of first (D1), second (D2), third (D3) and fourth (D4) derivative spectrophotometric methods, CARB was determined by using D1, D2, D3 derivatives, while D1 and D2 were used for the determination of DIAZ. The recommended methods were verified using laboratory prepared mixtures and then successfully applied for the pharmaceutical formulations analysis of the cited drugs. The results obtained revealed the efficiency of the proposed methods as quantitative tool of analysis of the quaternary mixture with no requirement

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Publication Date
Wed Jan 01 2020
Journal Name
Biochemical And Cellular Archives
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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Publication Date
Thu Dec 01 2022
Journal Name
Baghdad Science Journal
Simultaneous Ratio Derivative Spectrophotometric Determination of Paracetamol, Caffeine and Ibuprofen in Their Ternary Form

A new, accurate, precise and economic two spectrophotometric methods for determination of Paracetamol (Par), Ibuprofen (Ibu), and Caffeine (Caf) were suggested. Those methods were the first and second ratio derivative spectrum using a double devisor. Par, Ibu, and Caf showed many useful peaks for their quantified determination. The validity of all analysis modes for determination of the three compounds, peak to baseline, peak area and peak to peak were according to ICH. The linearity of two methods was between 5 µg/ml as a lower concentration and 50 µg/ml as the highest concentration for three compounds. Recovery percentage was around 100% and relative standard deviation was less than 2.6%. The methods were applied successfully in the

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Publication Date
Mon May 08 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Evaluation Of liver And Kidney Functions In Lung And Bladder Cancer Patients

This study was performed at Nuclear Radiation Hospital in Baghdad for the period from
January 2011 to May 2011. 44 Blood samples were collected from patients suffered lung and
bladder cancer and 24 samples as healthy control individuals.
Routine liver functions tests were studied by measuring S.GPT, S.GOT and Kidney
function was evaluated by estimation of blood urea and creatinine in serum samples of
individuals studied.
It was observed that the incidence of lung and bladder cancer was higher in males than
females patients ( male 81.82 %, 72.73%, female18 .18%, 27.27% respectively).
Insignificant difference was noted among age of lung and bladder cancer patients
compared with control group. The results

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Publication Date
Sun Sep 05 2010
Journal Name
Baghdad Science Journal
Volterra Runge- Kutta Methods for Solving Nonlinear Volterra Integral Equations

In this paper Volterra Runge-Kutta methods which include: method of order two and four will be applied to general nonlinear Volterra integral equations of the second kind. Moreover we study the convergent of the algorithms of Volterra Runge-Kutta methods. Finally, programs for each method are written in MATLAB language and a comparison between the two types has been made depending on the least square errors.

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Publication Date
Tue Mar 30 2021
Journal Name
Baghdad Science Journal
Solving Fractional Damped Burgers' Equation Approximately by Using The Sumudu Transform (ST) Method

       In this work, the fractional damped Burger's equation (FDBE) formula    = 0,

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Publication Date
Sat Dec 30 2023
Journal Name
Iraqi Journal Of Science
Numerical Approximations of a One-Dimensional Time-Fractional Semilinear Parabolic Equation

     The time fractional order differential equations are fundamental tools that are used for modeling neuronal dynamics. These equations are obtained by substituting the time derivative of order  where , in the standard equation with the Caputo fractional formula. In this paper, two implicit difference schemes: the linearly Euler implicit and the Crank-Nicolson (CN) finite difference schemes, are employed in solving a one-dimensional time-fractional semilinear equation with Dirichlet boundary conditions. Moreover, the consistency, stability and convergence of the proposed schemes are investigated. We prove that the IEM is unconditionally stable, while CNM is conditionally stable. Furthermore, a comparative study between these two s

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Publication Date
Tue Jun 01 2021
Journal Name
Baghdad Science Journal
Reliability and Failure Probability Functions of the m-Consecutive-k-out-of-n: F Linear and Circular Systems

The m-consecutive-k-out-of-n: F linear and circular system consists of n sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least m non-overlapping runs of consecutive-k failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly m-consecutive-k-out-of-n: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided.

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Publication Date
Wed Feb 28 2024
Journal Name
Al-rafidain Journal Of Medical Sciences ( Issn 2789-3219 )
The Effects of -806 T/C and -857 T/C Single Nucleotide Polymorphisms in the TNF-α Gene on Rheumatoid Arthritis Severity and Inflammatory Markers

Background: Polymorphisms in the TNF-α gene affect the development and progression of rheumatoid arthritis. Objective: To investigate the associations between (-806 T/C) and (-857 T/C) SNPs with rheumatoid arthritis severity and susceptibility in a sample of Iraqi patients. Methods: A case-control study was conducted in Baghdad, Iraq. Twenty healthy controls and 63 patients confirmed to be newly diagnosed with rheumatoid arthritis were included. Those are divided into two groups (patients and controls), and the patients were further subdivided into severe and mild-moderate groups. Samples from those participants were analyzed for clinical and inflammatory parameter measurements. Genotyping by the Sanger method was performed to stu

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Publication Date
Fri Jan 01 2016
Journal Name
International Journal Of Mathematics Trends And Technology (ijmtt)