Numerical solutions of fractional differential equations by using fractional explicit Adams method
Differential equations of fractional order are believed to be more challenging to compute compared to the integer-order differential equations due to its arbitrary properties. This study proposes a multistep method to solve fractional differential equations. The method is derived based on the concep...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Multidisciplinary Digital Publishing Institute
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/86935/ http://psasir.upm.edu.my/id/eprint/86935/1/Numerical%20solutions%20of%20fractional%20differential%20equations.pdf |
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| author | Zabidi, Nur Amirah Abdul Majid, Zanariah Kilicman, Adem Rabiei, Faranak |
| author_facet | Zabidi, Nur Amirah Abdul Majid, Zanariah Kilicman, Adem Rabiei, Faranak |
| author_sort | Zabidi, Nur Amirah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Differential equations of fractional order are believed to be more challenging to compute compared to the integer-order differential equations due to its arbitrary properties. This study proposes a multistep method to solve fractional differential equations. The method is derived based on the concept of a third-order Adam–Bashforth numerical scheme by implementing Lagrange interpolation for fractional case, where the fractional derivatives are defined in the Caputo sense. Furthermore, the study includes a discussion on stability and convergence analysis of the method. Several numerical examples are also provided in order to validate the reliability and efficiency of the proposed method. The examples in this study cover solving linear and nonlinear fractional differential equations for the case of both single order as α∈(0,1) and higher order, α∈[1,2), where α denotes the order of fractional derivatives of Dαy(t). The comparison in terms of accuracy between the proposed method and other existing methods demonstrate that the proposed method gives competitive performance as the existing methods. |
| first_indexed | 2025-11-15T12:43:26Z |
| format | Article |
| id | upm-86935 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:43:26Z |
| publishDate | 2020 |
| publisher | Multidisciplinary Digital Publishing Institute |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-869352022-01-07T08:43:52Z http://psasir.upm.edu.my/id/eprint/86935/ Numerical solutions of fractional differential equations by using fractional explicit Adams method Zabidi, Nur Amirah Abdul Majid, Zanariah Kilicman, Adem Rabiei, Faranak Differential equations of fractional order are believed to be more challenging to compute compared to the integer-order differential equations due to its arbitrary properties. This study proposes a multistep method to solve fractional differential equations. The method is derived based on the concept of a third-order Adam–Bashforth numerical scheme by implementing Lagrange interpolation for fractional case, where the fractional derivatives are defined in the Caputo sense. Furthermore, the study includes a discussion on stability and convergence analysis of the method. Several numerical examples are also provided in order to validate the reliability and efficiency of the proposed method. The examples in this study cover solving linear and nonlinear fractional differential equations for the case of both single order as α∈(0,1) and higher order, α∈[1,2), where α denotes the order of fractional derivatives of Dαy(t). The comparison in terms of accuracy between the proposed method and other existing methods demonstrate that the proposed method gives competitive performance as the existing methods. Multidisciplinary Digital Publishing Institute 2020-10-01 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/86935/1/Numerical%20solutions%20of%20fractional%20differential%20equations.pdf Zabidi, Nur Amirah and Abdul Majid, Zanariah and Kilicman, Adem and Rabiei, Faranak (2020) Numerical solutions of fractional differential equations by using fractional explicit Adams method. Mathematics, 8 (10). pp. 1-25. ISSN 2227-7390 https://www.mdpi.com/2227-7390/8/10/1675 10.3390/math8101675 |
| spellingShingle | Zabidi, Nur Amirah Abdul Majid, Zanariah Kilicman, Adem Rabiei, Faranak Numerical solutions of fractional differential equations by using fractional explicit Adams method |
| title | Numerical solutions of fractional differential equations by using fractional explicit Adams method |
| title_full | Numerical solutions of fractional differential equations by using fractional explicit Adams method |
| title_fullStr | Numerical solutions of fractional differential equations by using fractional explicit Adams method |
| title_full_unstemmed | Numerical solutions of fractional differential equations by using fractional explicit Adams method |
| title_short | Numerical solutions of fractional differential equations by using fractional explicit Adams method |
| title_sort | numerical solutions of fractional differential equations by using fractional explicit adams method |
| url | http://psasir.upm.edu.my/id/eprint/86935/ http://psasir.upm.edu.my/id/eprint/86935/ http://psasir.upm.edu.my/id/eprint/86935/ http://psasir.upm.edu.my/id/eprint/86935/1/Numerical%20solutions%20of%20fractional%20differential%20equations.pdf |