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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 Jul 28 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Fractional Chemical Composition of Asphalt as a Function of Its Durability

In order to get better understanding of asphalt pavement performance, asphalt from five Iraqi refineries (Qayarah, Nassiriyah, Baiji, Samawah and Daurah) were analyzed into five chemical fractions including asphaltenes, polar compounds, first acidaffins, second acidaffins and saturated hydrocarbons where the last four fractions called maltenes. Polar compounds /saturated hydrocarbons ratio (PC/S) and the ratio of the reactive to the unreactive components of the maltenes fraction (durability rating) parameters were determined. The study showed that Baiji asphalt has the best durability over other asphalts, while Qayarah asphalt is considered to have the least durability grade. These results confirm the correlation of the chemical composit

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Publication Date
Sat Feb 27 2021
Journal Name
Iraqi Journal Of Science
Asymptotic Stability for Some Types of Nonlinear Fractional Order Differential-Algebraic Control Systems

The aim of this paper is to study the asymptotically stable solution of nonlinear single and multi fractional differential-algebraic control systems, involving feedback control inputs, by an effective approach that depends on necessary and sufficient conditions.

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Publication Date
Thu Sep 30 2021
Journal Name
Iraqi Journal Of Science
A Study of a Certain Family of Multivalent Functions Associated with Subordination

The aim of this paper is to introduce a certain family of new classes of multivalent functions associated with subordination. The various results obtained here for each of these classes include coefficient estimates radius of convexity, distortion and growth theorem.  

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Publication Date
Mon May 04 2009
Journal Name
Journal Of Al-nahrain University
Solution of two-dimensional fractional order volterra integro-differential equations

In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.

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Publication Date
Fri Aug 20 2021
Journal Name
Iraqi Journal Of Laser
Fractional CO2 Laser for Treatment of Female Stress Urinary Incontinence

Background: Urinary incontinence (UI) is a common disorder that affects women of various ages and impacts all aspects of life. This condition negatively influences quality of life. Fractional CO2 laser (10600nm) is the recent method for treatment of stress urinary incontinence in women. Objectives: The purpose of the study was to evaluate the efficacy and safety of fractional CO2 laser (10600nm) in the treatment of female stress urinary incontinence. Materials & Methods: This study was done from July 2020 to February 2021conducted at the laser institute for postgraduate studies university of Baghdad, patients collected from a private clinic and the Department of

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Publication Date
Thu Jun 01 2023
Journal Name
Partial Differential Equations In Applied Mathematics
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Publication Date
Sun Jun 07 2015
Journal Name
Baghdad Science Journal
A Solution of Second Kind Volterra Integral Equations Using Third Order Non-Polynomial Spline Function

In this paper, third order non-polynomial spline function is used to solve 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of this method, and to compare the computed results with other known methods.

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Publication Date
Sat Feb 27 2021
Journal Name
Iraqi Journal Of Science
Hille and Nehari Type Oscillation Criteria for Conformable Fractional Differential Equations

In this paper, we develop the Hille and Nehari Type criteria for the oscillation of all solutions to the Fractional Differential Equations involving Conformable fractional derivative. Some new oscillatory criteria are obtained by using the Riccati transformations and comparison technique. We show the validity and effectiveness of our results by providing various examples.

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Publication Date
Tue Jun 18 2024
Journal Name
2024 Ieee 33rd International Symposium On Industrial Electronics (isie)
An Adaptive Integral Sliding Mode Control for Disturbed Servo Motor Systems

Abstract-Servo motors are important parts of industry automation due to their several advantages such as cost and energy efficiency, simple design, and flexibility. However, the position control of the servo motor is a difficult task because of different factors of external disturbances, nonlinearities, and uncertainties. To tackle these challenges, an adaptive integral sliding mode control (AISMC) is proposed, in which a novel bidirectional adaptive law is constructed to reduce the control chattering. The proposed control has three steps to be designed. Firstly, a full-order integral sliding manifold is designed to improve the servo motor position tracking performance, in which the reaching phase is eliminated to achieve the invariance of

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Publication Date
Fri Nov 01 2024
Journal Name
Cytokine
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