New Algorithms for Dealing with Fractional Initial Value Problems
This work purposes to establish two small numerical modifications for the Fractional Euler method (FEM) and the Modified Fractional Euler Method (MFEM) to deal with fractional initial value problems. Two such modifications, which are named Improved Modified Fractional Euler Method 1 (IMFEM 1) and Im...
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| Format: | Article |
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MDPI AG
2023-05-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/5/488 |
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| author | Iqbal M. Batiha Ahmad A. Abubaker Iqbal H. Jebril Suha B. Al-Shaikh Khaled Matarneh |
| author_facet | Iqbal M. Batiha Ahmad A. Abubaker Iqbal H. Jebril Suha B. Al-Shaikh Khaled Matarneh |
| author_sort | Iqbal M. Batiha |
| collection | DOAJ |
| description | This work purposes to establish two small numerical modifications for the Fractional Euler method (FEM) and the Modified Fractional Euler Method (MFEM) to deal with fractional initial value problems. Two such modifications, which are named Improved Modified Fractional Euler Method 1 (IMFEM 1) and Improved Modified Fractional Euler Method 2 (IMFEM 2), endeavor to further enhance FEM and MFEM in terms of attaining more accuracy. By utilizing certain theoretical results, the resultant error bounds of the proposed methods are analyzed and estimated. Several numerical comparisons are carried out to validate the efficiency of our proposed methods. |
| first_indexed | 2024-03-11T03:56:50Z |
| format | Article |
| id | doaj.art-90a6ff93cf764d4485aa98f3ca3234e3 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T03:56:50Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-90a6ff93cf764d4485aa98f3ca3234e32023-11-18T00:27:59ZengMDPI AGAxioms2075-16802023-05-0112548810.3390/axioms12050488New Algorithms for Dealing with Fractional Initial Value ProblemsIqbal M. Batiha0Ahmad A. Abubaker1Iqbal H. Jebril2Suha B. Al-Shaikh3Khaled Matarneh4Department of Mathematics, Al Zaytoonah University, Amman 11733, JordanFaculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi ArabiaDepartment of Mathematics, Al Zaytoonah University, Amman 11733, JordanFaculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi ArabiaFaculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi ArabiaThis work purposes to establish two small numerical modifications for the Fractional Euler method (FEM) and the Modified Fractional Euler Method (MFEM) to deal with fractional initial value problems. Two such modifications, which are named Improved Modified Fractional Euler Method 1 (IMFEM 1) and Improved Modified Fractional Euler Method 2 (IMFEM 2), endeavor to further enhance FEM and MFEM in terms of attaining more accuracy. By utilizing certain theoretical results, the resultant error bounds of the proposed methods are analyzed and estimated. Several numerical comparisons are carried out to validate the efficiency of our proposed methods.https://www.mdpi.com/2075-1680/12/5/488fractional differential equationsfractional Euler methodCaputo fractional derivative operator |
| spellingShingle | Iqbal M. Batiha Ahmad A. Abubaker Iqbal H. Jebril Suha B. Al-Shaikh Khaled Matarneh New Algorithms for Dealing with Fractional Initial Value Problems Axioms fractional differential equations fractional Euler method Caputo fractional derivative operator |
| title | New Algorithms for Dealing with Fractional Initial Value Problems |
| title_full | New Algorithms for Dealing with Fractional Initial Value Problems |
| title_fullStr | New Algorithms for Dealing with Fractional Initial Value Problems |
| title_full_unstemmed | New Algorithms for Dealing with Fractional Initial Value Problems |
| title_short | New Algorithms for Dealing with Fractional Initial Value Problems |
| title_sort | new algorithms for dealing with fractional initial value problems |
| topic | fractional differential equations fractional Euler method Caputo fractional derivative operator |
| url | https://www.mdpi.com/2075-1680/12/5/488 |
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