An Accurate Approach to Simulate the Fractional Delay Differential Equations
The fractional Legendre polynomials (FLPs) that we present as an effective method for solving fractional delay differential equations (FDDEs) are used in this work. The Liouville–Caputo sense is used to characterize fractional derivatives. This method uses the spectral collocation technique based on...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/9/671 |
| _version_ | 1797580041229434880 |
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| author | Mohamed Adel Mohamed M. Khader Salman Algelany Khaled Aldwoah |
| author_facet | Mohamed Adel Mohamed M. Khader Salman Algelany Khaled Aldwoah |
| author_sort | Mohamed Adel |
| collection | DOAJ |
| description | The fractional Legendre polynomials (FLPs) that we present as an effective method for solving fractional delay differential equations (FDDEs) are used in this work. The Liouville–Caputo sense is used to characterize fractional derivatives. This method uses the spectral collocation technique based on FLPs. The proposed method converts FDDEs into a set of algebraic equations. We lay out a study of the convergence analysis and figure out the upper bound on error for the approximate solution. Examples are provided to demonstrate the precision of the suggested approach. |
| first_indexed | 2024-03-10T22:44:41Z |
| format | Article |
| id | doaj.art-b67172b5e26747d6ad55bd361ac4390a |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T22:44:41Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-b67172b5e26747d6ad55bd361ac4390a2023-11-19T10:48:33ZengMDPI AGFractal and Fractional2504-31102023-09-017967110.3390/fractalfract7090671An Accurate Approach to Simulate the Fractional Delay Differential EquationsMohamed Adel0Mohamed M. Khader1Salman Algelany2Khaled Aldwoah3Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina 42210, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Islamic University of Madinah, Medina 42210, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Islamic University of Madinah, Medina 42210, Saudi ArabiaThe fractional Legendre polynomials (FLPs) that we present as an effective method for solving fractional delay differential equations (FDDEs) are used in this work. The Liouville–Caputo sense is used to characterize fractional derivatives. This method uses the spectral collocation technique based on FLPs. The proposed method converts FDDEs into a set of algebraic equations. We lay out a study of the convergence analysis and figure out the upper bound on error for the approximate solution. Examples are provided to demonstrate the precision of the suggested approach.https://www.mdpi.com/2504-3110/7/9/671FDDEsorthogonal systemspectral collocation techniqueconvergence analysisfractional-order Legendre polynomials |
| spellingShingle | Mohamed Adel Mohamed M. Khader Salman Algelany Khaled Aldwoah An Accurate Approach to Simulate the Fractional Delay Differential Equations Fractal and Fractional FDDEs orthogonal system spectral collocation technique convergence analysis fractional-order Legendre polynomials |
| title | An Accurate Approach to Simulate the Fractional Delay Differential Equations |
| title_full | An Accurate Approach to Simulate the Fractional Delay Differential Equations |
| title_fullStr | An Accurate Approach to Simulate the Fractional Delay Differential Equations |
| title_full_unstemmed | An Accurate Approach to Simulate the Fractional Delay Differential Equations |
| title_short | An Accurate Approach to Simulate the Fractional Delay Differential Equations |
| title_sort | accurate approach to simulate the fractional delay differential equations |
| topic | FDDEs orthogonal system spectral collocation technique convergence analysis fractional-order Legendre polynomials |
| url | https://www.mdpi.com/2504-3110/7/9/671 |
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