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Article
SOLUTION OF MULTI-DELAY OF LINEAR INTEGRO-DIFFERENTIALEQUATIONS USING WALSH FUNCTIONS

Author: Ahmed Ayyoub Yousif
Journal: Al-Nahrain Journal of Science مجلة النهرين للعلوم ISSN: (print)26635453,(online)26635461 Year: 2009 Volume: 12 Issue: 4 Pages: 156-162
Publisher: Al-Nahrain University جامعة النهرين

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Abstract

A matrix, called the "delay operational matrix", is constructed from the Walsh matrix, this matrix, together with some matrices obtained from the delay operational matrix after performing right-shift operations, is used to solve the multi-delay linear integro-differential equations (Fredholm and Volterra). Examples are given to compare between the exact and the approximate solution that obtained by using this method.

المصفوفة المعرفة بـ"مصفوفة العمليات التباطئية" والتي نستطيع بنائها باستخدام مصفوفة والش. هذه المصفوفة مع مصفوفات اخرى ناتجة عن مصفوفة العمليات التباطئية بعد عملية التزحيف الصحيحة استعملت لحل المعادلات التفاضلية التكاملية الخطية المتعددة التباطئ بنوعيها (الفريدهولم و الفولتيرا). تم اعطاء امثلة لتوضيح هذه الطريقة مع مقارنه بين الحل المضبوط و الحل الناتج من هذه الطريقة.

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Article
About Fractional Operators: Behavior and Extension

Authors: Ahmed Ayyoub Yousif --- Alauldin Noori Ahmed
Journal: Diyala Journal For Pure Science مجلة ديالى للعلوم الصرفة ISSN: 83732222 25189255 Year: 2011 Volume: 7 Issue: 4 Pages: 1-15
Publisher: Diyala University جامعة ديالى

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Abstract

In this paper, we are study some behavior fractional operators solutions, such as existence, uniqueness, stabilities and extended formulas for a dynamic multi-fractional order differential equations. Theorems are stated and proved based on the definitions of Riemann-Liouville fractional integral and Grunwald-Letnikov fractional derivative. Also, a simple numerical approach has been implemented to solve such system.

في هذا البحث تم دراسة سلوك بعض مشغلي حلول جزئية، مثل التفرد، وجود، بثبات والصيغ الموسعة لدينامية متعددة المعادلات التفاضلية الجزئية. وذكر النظريات، وأثبتت بناء على تعريف ريمان، يوفيل لا يتجزأ كسور وجرونوالد-Letnikov مشتق كسور. أيضا، تم تنفيذ نهج عددية بسيطة في حل مثل هذا النظام.


Article
Numerical Solution for Fractional Order Space-Time Burger's Equation Using Legendre Wavelet - Chebyshev Wavelet Spectral Collocation Method

Authors: Osama H. Mohammed --- Mohammed G. S. AL-Safi --- Ahmed Ayyoub Yousif
Journal: Al-Nahrain Journal of Science مجلة النهرين للعلوم ISSN: (print)26635453,(online)26635461 Year: 2018 Volume: 21 Issue: 1 Pages: 121-127
Publisher: Al-Nahrain University جامعة النهرين

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Abstract

In this article, a Legendre wavelet- Chebyshev wavelet spectral collocation method is proposed for solving fractional order space-time Burger's equation with the Legendre wavelet and Chebyshev wavelet operational matrices of fractional derivatives. The fractional derivative is described in the Caputo sense. The proposed method is based on Legendre wavelet-Chebyshev wavelet for space and time variables respectively. This method will reduc the problem under consideration to the solution of nonlinear algebraic equations. In order to confirm the efficiency of the proposed method, two numerical examples are implemented and comparing the numerical solution with the exact one, as well as, of other methods in given literatures, we demonstrate the high accuracy and efficiency of the proposed method.


Article
Analyzing Cryptosystems by Using Artificial Intelligence

Authors: Ahmed Ayyoub Yousif --- Mohammed G. S. Al-Safi --- Faez Hassan Ali
Journal: Al-Nahrain Journal of Science مجلة النهرين للعلوم ISSN: (print)26635453,(online)26635461 Year: 2018 Volume: 00 Issue: 1 Pages: 100-108
Publisher: Al-Nahrain University جامعة النهرين

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Abstract

This paper aims to apply the Bees Algorithm for solving system of equations. The solving System of Equations may be linear or nonlinear for a number of unknowns. As an application of System of Equations, we can implement cryptanalysis attack algorithms on stream cipher systems using plaintext attack (or part from it). We consider the Geffe System (which has nonlinear combining function) to be our study case, which is depend on set of Linear Feedback Shift Registers, as a model of stream cipher systems, in the performance of Bees Algorithm by solving System of Equations for any number of variables of the output of Linear Feedback Shift Registers.The application divided into two stages, first, constructing System of Equations for the suggested cryptosystem, and the second, is attacking the variables of System of Equations which they are also represent the initial key values of the combined of Linear Feedback Shift Registers.

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