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Towards Solving Fractional Order Delay Variational Problems Using Euler Polynomial Operational Matrices
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     In this paper, we introduce an approximate method for solving fractional order delay variational problems using fractional Euler polynomials operational matrices. For this purpose, the operational matrices of fractional integrals and derivatives are designed for Euler polynomials. Furthermore, the delay term in the considered functional is also decomposed in terms of the operational matrix of the fractional Euler polynomials. It is applied and substituted together with the other matrices of the fractional integral and derivative into the suggested functional. The main equations are then reduced to a system of algebraic equations. Therefore, the desired solution to the original variational problem is obtained by solving the resulting system. Error analysis has been discussed. An illustrative example is given in order to illustrate that the proposed method is very accurate and efficient for solving such kinds of problems.

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Publication Date
Sun Dec 05 2010
Journal Name
Baghdad Science Journal
Stability of Nonlinear Systems of Fractional Order Differential Equations
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In this paper, a sufficient condition for stability of a system of nonlinear multi-fractional order differential equations on a finite time interval with an illustrative example, has been presented to demonstrate our result. Also, an idea to extend our result on such system on an infinite time interval is suggested.

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Publication Date
Mon Mar 08 2021
Journal Name
Baghdad Science Journal
First Order Nonlinear Neutral Delay Differential Equations
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The author obtain results on the asymptotic behavior of the nonoscillatory solutions of first order nonlinear neutral differential equations. Keywords. Neutral differential equations, Oscillatory and Nonoscillatory solutions.

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Publication Date
Wed Nov 30 2022
Journal Name
Iraqi Journal Of Science
Optimal Harvesting Strategy of a Discretization Fractional-Order Biological Model
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     Optimal control methods are used to get an optimal policy for harvesting renewable resources. In particular, we investigate a discretization fractional-order biological model, as well as its behavior through its fixed points, is analyzed. We also employ the maximal Pontryagin principle to obtain the optimal solutions. Finally, numerical results confirm our theoretical outcomes.

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Publication Date
Thu Jul 25 2019
Journal Name
Advances In Intelligent Systems And Computing
Solving Game Theory Problems Using Linear Programming and Genetic Algorithms
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Publication Date
Wed Mar 30 2022
Journal Name
Iraqi Journal Of Science
Numerical Solution of Linear Fractional Differential Equation with Delay Through Finite Difference Method
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This article addresses a new numerical method to find a numerical solution of the linear delay differential equation of fractional order , the fractional derivatives described in the Caputo sense. The new approach is to approximating second and third derivatives. A backward finite difference method is used. Besides, the composite Trapezoidal rule is used in the Caputo definition to match the integral term. The accuracy and convergence of the prescribed technique are explained. The results  are shown through numerical examples.

 

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Publication Date
Mon Jun 22 2020
Journal Name
Baghdad Science Journal
Phase Fitted And Amplification Fitted Of Runge-Kutta-Fehlberg Method Of Order 4(5) For Solving Oscillatory Problems
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In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method.

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Publication Date
Sun Jul 29 2018
Journal Name
Iraqi Journal Of Science
A new approximate solution for the Telegraph equation of space-fractional order derivative by using Sumudu method
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In this work, we are concerned with how to find an explicit approximate solution (AS) for the telegraph equation of space-fractional order (TESFO) using Sumudu transform method (STM). In this method, the space-fractional order derivatives are defined in the Caputo idea. The Sumudu method (SM) is established to be reliable and accurate. Three examples are discussed to check the applicability and the simplicity of this method. Finally, the Numerical results are tabulated and displayed graphically whenever possible to make comparisons between the AS and exact solution (ES).

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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
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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
Sat Oct 01 2022
Journal Name
Journal Of Computational Science
Novel approximate solution for fractional differential equations by the optimal variational iteration method
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Publication Date
Sat Oct 01 2022
Journal Name
Journal Of Computational Science
Novel approximate solution for fractional differential equations by the optimal variational iteration method
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