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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 Jan 26 2024
Journal Name
Iraqi Journal Of Science
Effect of Mhd on Accelerated Flows of A Viscoelastic Fluid with The Fractional Burgers’ Model

In this paper, we studied the effect of magnetic hydrodynamic (MHD) on accelerated flows of a viscoelastic fluid with the fractional Burgers’ model. The velocity field of the flow is described by a fractional partial differential equation of fractional order by using Fourier sine transform and Laplace transform, an exact solutions for the velocity distribution are obtained for the following two problems: flow induced by constantly accelerating plate, and flow induced by variable accelerated plate. These solutions, presented under integral and series forms in terms of the generalized Mittag-Leffler function, are presented as the sum of two terms. The first term, represent the velocity field corresponding to a Newtonian fluid, and the se

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Publication Date
Sat Jun 27 2020
Journal Name
Iraqi Journal Of Science
On Analytical Solution of Time-Fractional Type Model of the Fisher’s Equation

In this paper, the time-fractional Fisher’s equation (TFFE) is considered to exam the analytical solution using the Laplace q-Homotopy analysis method (Lq-HAM)”. The Lq-HAM is a combined form of q-homotopy analysis method (q-HAM) and Laplace transform. The aim of utilizing the Laplace transform is to outdo the shortage that is mainly caused by unfulfilled conditions in the other analytical methods. The results show that the analytical solution converges very rapidly to the exact solution.

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Publication Date
Sun Feb 03 2019
Journal Name
Journal Of The College Of Education For Women
The Semilogy of the Narrative Structure in "Nisa'a Al Altabat" Novel: The Semilogy of the Narrative Structure in "Nisa'a Al Altabat" Novel

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This recearch is about studying the novel (doorstep’s women) by the Iraqi
narrator Hadia Hussian, and I choose Semiolog as a Curriculum for this
critical approach, because I think that this Semiotic curriculum has the ability
to read the Subjects and the narrative constructions. Which form the structure
of the novel starting from the little to the characters.
The focus is on many narrative constructions in the novel we have
studied the semiology of the tittle, the semiology of the cover, of the color, the
names of the characters and the semiology of the female characters.
First the focus of the novel is on the women’s characters because most
of it’s characters are women. Secondly because these

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Publication Date
Thu Dec 01 2022
Journal Name
Baghdad Science Journal
Synthesis, Characterization, and Investigation the Inhibitory Impact of Thiosemicarbazide Derivative toward the Corrosion of Mild Steel in Acidic Media

        In this study we focused on the determination of influence the novel synthesized thiosemicarbazide derivative "2-(2-hydroxy-3-methoxybenzylidene) hydrazinecarbothioamide" (HMHC) influenced the corrosion inhibition of mild steel (MS) in a 1.0 M hydrochloric acid acidic solution.This is in an effort to preserve the metal material by maintaining it from corrosion.The synthesized inhibitor was characterized using elemental analysis, and NMR-spectroscopy. Then the corrosion inhibition capability of (HMHC) was studied on mild steel in an acidic medium by weight loss technique within variables [temperature, inhibitor concentration, and time]. The immersion periods were [1:00, 3:00, 5:00, 10:00, 24:00, and 72:00] hours and the tem

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Publication Date
Tue Jan 01 2019
Journal Name
Sci.int.(lahore)
FILTER BASES AND SUPRA PERFECT FUNCTIONS

We introduce some new generalizations of some definitions which are, supra closure converge to a point, supra closure directed toward a set, almost supra converges to a set, almost supra cluster point, a set supra H-closed relative, supra closure continuous functions, supra weakly continuous functions, supra compact functions, supra rigid a set, almost supra closed functions and supra perfect functions. And we state and prove several results concerning it

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Publication Date
Fri Jan 01 2010
Journal Name
Journal Of Collage Of Education
FILTER BASES AND ω-PERFECT FUNCTIONS

In this paper introduce some generalizations of some definitions which are, closure converge to a point, closure directed toward a set, almost ω-converges to a set, almost condensation point, a set ωH-closed relative, ω-continuous functions, weakly ω-continuous functions, ω-compact functions, ω-rigid a set, almost ω-closed functions and ω-perfect functions with several results concerning them.

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Publication Date
Mon Mar 08 2021
Journal Name
Baghdad Science Journal
on periodic point and chaotic functions

We dealt with the nature of the points under the influence of periodic function chaotic functions associated functions chaotic and sufficient conditions to be a very chaotic functions Palace

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Publication Date
Wed Dec 01 2021
Journal Name
Baghdad Science Journal
Boubaker Wavelets Functions: Properties and Applications

This paper is concerned with introducing an explicit expression for orthogonal Boubaker polynomial functions with some important properties. Taking advantage of the interesting properties of Boubaker polynomials, the definition of Boubaker wavelets on interval [0,1) is achieved. These basic functions are orthonormal and have compact support. Wavelets have many advantages and applications in the theoretical and applied fields, and they are applied with the orthogonal polynomials to propose a new method for treating several problems in sciences, and engineering that is wavelet method, which is computationally more attractive in the various fields. A novel property of Boubaker wavelet function derivative in terms of Boubaker wavelet themsel

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Publication Date
Sat Jun 27 2020
Journal Name
Iraqi Journal Of Science
A Class of Harmonic Univalent Functions Defined by Differential Operator and the Generalization

In this paper, a new class of harmonic univalent functions was defined by the differential operator. We obtained some geometric properties, such as the coefficient estimates, convex combination, extreme points, and convolution (Hadamard product), which are required

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Publication Date
Thu Oct 26 2017
Journal Name
International Journal Of Pure And Applied Mathematics
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