Published January 1, 2018
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FRACTIONAL EULER METHOD; AN EFFECTIVE TOOL FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS
Description
Through this article, a numerical scheme based upon the modified fractional Euler method (MFEM) is introduced to find the numericalsolutions of linear and nonlinear systems of fractional differential equations (SFDEs) as well as nonlinear multi-order fractionaldifferential equations (MOFDEs). The fractional derivatives are defined by Caputo. The proposed algorithm is very simple and providesthe solutions directly without linearization, perturbations or any other assumptions. Illustrating examples with numerical comparisonsbetween the proposed algorithm and the exact and/or fourth order Runge Kutta method (RK4) are given to reveal the efficiency and theaccuracy of our algorithm.
Translated Descriptions
⚠️
This is an automatic machine translation with an accuracy of 90-95%
Translated Description (Arabic)
من خلال هذه المقالة، يتم تقديم مخطط رقمي يعتمد على طريقة أويلر الكسرية المعدلة (MFEM) لإيجاد الحلول العددية للأنظمة الخطية وغير الخطية للمعادلات التفاضلية الكسرية (SFDEs) وكذلك المعادلات التفاضلية الكسرية متعددة المستويات (MOFDEs). يتم تعريف المشتقات الكسرية بواسطة Caputo. الخوارزمية المقترحة بسيطة للغاية وتوفر الحلول مباشرة دون خطية أو اضطرابات أو أي افتراضات أخرى. يتم إعطاء أمثلة توضيحية مع مقارنات عددية بين الخوارزمية المقترحة وطريقة Runge Kutta الدقيقة و/أو الرابعة (RK4) للكشف عن كفاءة ودقة الخوارزمية الخاصة بنا.Translated Description (English)
Through this article, a numerical scheme based on the modified fractional Euler method (MFEM) is introduced to find the numerical solutions of linear and nonlinear systems of fractional differential equations (SFDEs) as well as nonlinear multi-order fractional differential equations (MOFDEs). The fractional derivatives are defined by Caputo. The proposed algorithm is very simple and provides the solutions directly without linearization, perturbations or any other assumptions. Illustrating examples with numerical comparisons between the proposed algorithm and the exact and/or fourth order Runge Kutta method (RK4) are given to reveal the efficiency and the accuracy of our algorithm.Translated Description (French)
Par cet article, un schéma numérique basé sur la méthode fractionnelle modifiée d'Euler (MFEM) est introduit pour trouver les solutions numériques des systèmes linéaires et non linéaires d'équations fractionnaires différentielles (SFDE) en tant qu'équations fractionnaires non linéaires à plusieurs ordres (MOFDE). Les dérivés fractionnaires sont définis par Caputo. The proposed algorithm is very simple and providesthe solutions directly without linearization, perturbations or any other assumptions. Illustrating examples with numerical comparisonsbetween the proposed algorithm and the exact and/or fourth order Runge Kutta method (RK4) are given to reveal the efficiency and theaccuracy of our algorithm.Translated Description (Spanish)
Through this article, a numerical scheme based upon the modified fractional Euler method (MFEM) is introduced to find the numericalsolutions of linear and nonlinear systems of fractional diferential equations (SFDEs) as well as nonlinear multi-order fractional diferential equations (MOFDEs). Los derivados fraccionales están definidos por Caputo. El algoritmo propuesto es muy simple y proporciona soluciones directamente sin linealización, perturbaciones o cualquier otra asunción. Illustrating examples with numerical comparisonsbetween the proposed algorithm and the exact and/or fourth order Runge Kutta method (RK4) are given to reveal the efficiency and theaccuracy of our algorithm.Files
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Additional details
Additional titles
- Translated title (Arabic)
- طريقة أويلر الكسرية ؛ أداة فعالة لحل المعادلات التفاضلية الكسرية
- Translated title (English)
- FRACTIONAL EULER METHOD; AN EFFECTIVE TOOL FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS
- Translated title (French)
- MÉTHODE FRACTIONAL EULER ; AN EFFECTIVE TOOL FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS
- Translated title (Spanish)
- FRACTIONAL EULER METHOD; AN EFFECTIVE TOOL FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS
Identifiers
- Other
- https://openalex.org/W2910143068
- DOI
- 10.21608/joems.2018.9460
References
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