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Article
Generalizing of Finite Difference Method for Certain Fractional Order Parabolic PDE’s

Authors: Eman Hassan Ouda --- Madeha Shaltagh Yousif --- Ahmed Mohamed Shukur --- Raghad Kadhim Salih
Journal: Journal of Al-Qadisiyah for Computer Science and Mathematics مجلة القادسية لعلوم الحاسوب والرياضيات ISSN: 20740204 / 25213504 Year: 2018 Volume: 10 Issue: 3 Pages: Math 41-53
Publisher: Al-Qadisiyah University جامعة القادسية

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Abstract

Space-time fractional differential equation with integral term (S-TFDE) has been considered.The finite difference method (implicit and explicit) combined with the trapezoidal integration formula has beenused tofind special formula to solve this equation. The stability and convergence have been discussed. The effect ofadding anintegral term to the common classical equation has been considered. Graphical representation of the calculatesolutions(obtained by the explicit and the implicit methods) for three numerical examples with their exact solution, areconsidered. All the calculations and graphs are designed with the help of MATLAB.


Article
Theorems on Certain Fractional Function and Derivative
نظریات في الدوال الكسریة الخاصة مع المشتقات

Authors: Ahmed Zain al-Abdin --- Maha Abd Al-Wahab
Journal: Engineering and Technology Journal مجلة الهندسة والتكنولوجيا ISSN: 16816900 24120758 Year: 2012 Volume: 30 Issue: 2 Pages: 261-264
Publisher: University of Technology الجامعة التكنولوجية

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Abstract

The aim of this paper is to prove the correctness of the relationI - I h (x) = h (x) for all xÎ(a, b],xaxa a aa a 00).

الھدف الرئیسي في ھذا البحث ھو برھان صحة العلاقةI - I h ( ) = h ( ) for all xÎ(a,b], 0 و( 0 |ha(x)| ≤ M


Article
Stability and Convergence of Explicit Difference Method for Solving the 3-Dimensional Two-Sided Fractional Diffusion Equation
الاستقراریة والتقارب لطریقة الفروق المنتھیة الصریحة لحَلّ معادلة الانتشار الكسریة ذات الاتجاھین الثلاثیة الابعادِ

Author: Iman Isho Gorial
Journal: Engineering and Technology Journal مجلة الهندسة والتكنولوجيا ISSN: 16816900 24120758 Year: 2012 Volume: 30 Issue: 5 Pages: 832-848
Publisher: University of Technology الجامعة التكنولوجية

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Abstract

In this paper, a numerical solution of the 3-dimensional two-sided fractionaldiffusion equation has been presented. The algorithm for the numerical solution forthis equation is based on explicit finite difference method. The consistency, conditionalstability, and convergence of the fractional order numerical method are described.The numerical method has been applied to solve a practical numerical example andthe results have been compared with exact solution. The results were presented intables using the MathCAD 12 software package when it is needed. The explicit finitedifference method appeared to be effective and reliable in solving the 3-dimensionaltwo-sided fractional Diffusion equation


Article
The Homotopy Analysis Method for Solving Multi- Fractional Order Integro-Differential Equations

Author: Ibtisam K. Hanan
Journal: Al-Nahrain Journal of Science مجلة النهرين للعلوم ISSN: (print)26635453,(online)26635461 Year: 2011 Volume: 14 Issue: 3 Pages: 139-143
Publisher: Al-Nahrain University جامعة النهرين

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Abstract

In this paper we use the homotopy analysis method to solve special types of the initial value problems that consist of multi-fractional order integro differential equation in which the fractional derivative and fractional integral in them are described in the Caputo sense and Riemann-Liouville sense respectively. Numerical examples are solved by using this method. These examples shows that high accuracy, simplicity and efficiency of this method

في هذا البحث استعملنا طريقة تحليل الهوموتوبي لحل انواع خاصة من مسائل القيم الابتدائية والتي تحتوي على المعادلات التفاضلية - التكاملية ذات الرتب الكسورية المزدوجة والتي تحتوي على المشتقة الكسورية من نوع كابوتو والتكامل الكسوري من نوع ريمان - ليوفييل. قمنا بحل بعض الامثلة العددية باستخدام هذه الطريقة. هذه الامثلة أضهرت دقة عالية، سهولة، كفاءة لهذه الطريقة.


Article
Local Existence Theorem of Fractional Differential Equations in Lp Space

Authors: Joseph Gh. Abdulahad --- Shayma A. Murad
Journal: AL-Rafidain Journal of Computer Sciences and Mathematics مجلة الرافدين لعلوم الحاسوب والرياضيات ISSN: 18154816 Year: 2012 Volume: 9 Issue: 2 Pages: 71-78
Publisher: Mosul University جامعة الموصل

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Abstract

We proved the existence of P-integrable solution in -space, where for the fractional differential equation which has the form: with boundary condition where is the Caputo fractional derivative, and c are positive constants with . The contraction mapping principle has been used to establish our main result.

في هذا البحث تمت دراسة وجود الحل للمعادلة التفاضلية المعممة من الرتبة في الفضاء حيث والتي لها الصيغة مع شرط مقيد حيث هي مشتقة كابوتو الكسرية، و c ثوابت موجبة مع . وقد استخدم مبدأ التطبيق الانكماشي لتأسيس النتائج الرئيسية.


Article
Solving Fuzzy Fractional Boundary Value Problems Using Fractional Differential Transform Method

Authors: Osama H. Mohammed --- Salam A. Ahmed
Journal: Al-Nahrain Journal of Science مجلة النهرين للعلوم ISSN: (print)26635453,(online)26635461 Year: 2013 Volume: 16 Issue: 4 Pages: 225-232
Publisher: Al-Nahrain University جامعة النهرين

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Abstract

In this paper we shall present an approximate solution for fuzzy fractional boundary value problems (FFBVP's) based on the Fractional Differential Transform Method (FDTM) which is proposed to solve linear and nonlinear FFBVP,s. The fuzziness will appear in the boundary conditions, to be fuzzy numbers. The solution of our model equations are calculated in the form of convergent series with easily computable components. Some examples are solved as an illustrations, the numerical results shows that the followed approach is easy to implement and accurate when applied to FFBVP,s.

في هذا البحث قدمنا الحل التقريبي لمسائل القيم الحدودية الضبابية ذات الرتب الكسرية بألاعتماد على طريقة تحويل التفاضلات الكسرية والتي استخدمت لحل مسائل القيم الحدودية الضبابية ذات الرتب الكسرية الخطية واللاخطية. الشروط الحدودية في هذه المسائل سوف تكون عبارة عن اعداد ضبابية. الحل لهذا النوع من المسائل سوف يتم حسابه على شكل متسلسلة متقاربة سهلة الحساب. تم حل بعض الامثلة كتوضيح للطريقة. النتائج التي تم الحصول عليها تظهر ان الطريقة سهلة التطبيق وعالية الدقة عند تطبيقها لحل مسائل القيم الحدودية الضبابية ذات الرتب الكسرية.


Article
A New Double Sumudu Transform Iterative Method for Solving Some of Fractional Partial Differential Equations

Authors: Hasan Shather Kadhem --- Samear Qasim Hasan
Journal: Journal of Education for Pure Science مجلة التربية للعلوم الصرفة ISSN: 20736592 Year: 2019 Volume: 9 Issue: 2 Pages: 158-171
Publisher: Thi-Qar University جامعة ذي قار

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Abstract

Abstract:In this paper, we apply double sumudu transform coupled with a numerical method ”a new iterativemethod” to solve some of fractional partial differential equations which cannot be solved by applyingdouble Sumudu transform only. Several examples illustrate with plotting their solutions are given.


Article
Algorithm to Solve Linear Volterra Fractional Integro-Differential Equation via Elzaki Transform

Author: Amaal A. Mohammed
Journal: Ibn Al-Haitham Journal For Pure And Applied Science مجلة ابن الهيثم للعلوم الصرفة والتطبيقية ISSN: 16094042 Year: 2017 Volume: 30 Issue: 2 Pages: 192-201
Publisher: Baghdad University جامعة بغداد

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Abstract

In this work, Elzaki transform (ET) introduced by Tarig Elzaki is applied to solve linear Volterra fractional integro-differential equations (LVFIDE). The fractional derivative is considered in the Riemman-Liouville sense. The procedure is based on the application of (ET) to (LVFIDE) and using properties of (ET) and its inverse. Finally, some examples are solved to show that this is computationally efficient and accurate.

Keywords

integral --- differential --- Volterra --- fractional --- Elzaki.


Article
Numerical Solution of Ordinary Differential Equations of Fractional Order Using Variable Step Size Method

Authors: Hayder H. Khayoon --- Fadhel S. Fadhel
Journal: Al-Nahrain Journal of Science مجلة النهرين للعلوم ISSN: (print)26635453,(online)26635461 Year: 2018 Volume: 00 Issue: 1 Pages: 143-149
Publisher: Al-Nahrain University جامعة النهرين

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Abstract

The main objective from this paper is to introduce and derive three methods depending on fractional Euler’s method and improve the results modifying the approach by using variable step size method.


Article
Analytical Solutions of the One-Dimensional Volterra Integro-Differential Equations within Local Fractional Derivative

Authors: Hassan Kamil Jassim --- Ammar Ali Neamah
Journal: Journal of Kufa for Mathematics and Computer مجلة الكوفة للرياضيات والحاسوب ISSN: 11712076 Year: 2017 Volume: 4 Issue: 1 Pages: 46-50
Publisher: University of Kufa جامعة الكوفة

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Abstract

The one-dimensional Volterra Integro-Differential Equations of the second kind associated with local fractional derivative operators are investigated. Analytical solutions are obtained by using the local fractional variational Iteration method (LFVIM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

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