A Numerical Solution of Generalized Caputo Fractional Initial Value Problems
In this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM method was utilized to establish approximate series solutions. The presented technique is considered to be an extension to the original...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/4/332 |
| _version_ | 1797605399971495936 |
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| author | Rania Saadeh Mohamed A. Abdoon Ahmad Qazza Mohammed Berir |
| author_facet | Rania Saadeh Mohamed A. Abdoon Ahmad Qazza Mohammed Berir |
| author_sort | Rania Saadeh |
| collection | DOAJ |
| description | In this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM method was utilized to establish approximate series solutions. The presented technique is considered to be an extension to the original Adams–Bashforth–Moulton approach. Numerical simulations and figures are presented and discussed, in order to show the efficiency of the proposed method. In the future, we anticipate that the provided generalized Caputo fractional derivative and the suggested method will be utilized to create and simulate a wide variety of generalized Caputo-type fractional models. We have included examples to demonstrate the accuracy of the present method. |
| first_indexed | 2024-03-11T05:00:33Z |
| format | Article |
| id | doaj.art-dc3fa0e660e44b20b245ffd240b10edf |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T05:00:33Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-dc3fa0e660e44b20b245ffd240b10edf2023-11-17T19:19:42ZengMDPI AGFractal and Fractional2504-31102023-04-017433210.3390/fractalfract7040332A Numerical Solution of Generalized Caputo Fractional Initial Value ProblemsRania Saadeh0Mohamed A. Abdoon1Ahmad Qazza2Mohammed Berir3Department of Mathematics, Zarqa University, Zarqa 13110, JordanDepartment of Basic Sciences (Mathematics) Deanship of Common First Year, Shaqra University, Riyadh 15342, Saudi ArabiaDepartment of Mathematics, Zarqa University, Zarqa 13110, JordanDepartment of Mathematics, Faculty of Science, Bakht Al-Ruda University, Duwaym 28812, White Nile State, SudanIn this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM method was utilized to establish approximate series solutions. The presented technique is considered to be an extension to the original Adams–Bashforth–Moulton approach. Numerical simulations and figures are presented and discussed, in order to show the efficiency of the proposed method. In the future, we anticipate that the provided generalized Caputo fractional derivative and the suggested method will be utilized to create and simulate a wide variety of generalized Caputo-type fractional models. We have included examples to demonstrate the accuracy of the present method.https://www.mdpi.com/2504-3110/7/4/332numerical solutionthe Apc-ABM methodCaputo derivativechaos |
| spellingShingle | Rania Saadeh Mohamed A. Abdoon Ahmad Qazza Mohammed Berir A Numerical Solution of Generalized Caputo Fractional Initial Value Problems Fractal and Fractional numerical solution the Apc-ABM method Caputo derivative chaos |
| title | A Numerical Solution of Generalized Caputo Fractional Initial Value Problems |
| title_full | A Numerical Solution of Generalized Caputo Fractional Initial Value Problems |
| title_fullStr | A Numerical Solution of Generalized Caputo Fractional Initial Value Problems |
| title_full_unstemmed | A Numerical Solution of Generalized Caputo Fractional Initial Value Problems |
| title_short | A Numerical Solution of Generalized Caputo Fractional Initial Value Problems |
| title_sort | numerical solution of generalized caputo fractional initial value problems |
| topic | numerical solution the Apc-ABM method Caputo derivative chaos |
| url | https://www.mdpi.com/2504-3110/7/4/332 |
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