Fractional block method for the solution of fractional order differential equations
The construction of the fourth-order 2-point Fractional Block Backward Differentiation Formula (2FBBDF(4)) to solve the fractional order differential equations (FDEs) is presented in this paper. The method is developed using the fractional linear multistep method (FLMM) linked with the linear differ...
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| Format: | Article |
| Language: | English |
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Universiti Putra Malaysia
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/113152/ http://psasir.upm.edu.my/id/eprint/113152/1/113152.pdf |
| _version_ | 1848866142565695488 |
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| author | Noor, N.M. Yatim, S.A.M. Ibrahim, Z.B. |
| author_facet | Noor, N.M. Yatim, S.A.M. Ibrahim, Z.B. |
| author_sort | Noor, N.M. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The construction of the fourth-order 2-point Fractional Block Backward Differentiation Formula (2FBBDF(4)) to solve the fractional order differential equations (FDEs) is presented in this paper. The method is developed using the fractional linear multistep method (FLMM) linked with the linear difference operator. This paper aims to approximate the fractional order problems via 2FBBDF(4), which is normally used to solve ordinary differential equations. The criteria for the stability of the method are analyzed in order to solve FDE problems. Consequently, the method is determined to be A-stable for different values of α within the interval (0, 1). Then, Newton’s iteration is implemented in this method to solve the problems. Multiple numerical examples of linear, nonlinear, and system FDEs are provided for the scenario where the order α lies within the range of 0 and 1. Ultimately, the numerical results confirm that the proposed method performs at a similar level to the existing methods. |
| first_indexed | 2025-11-15T14:15:54Z |
| format | Article |
| id | upm-113152 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:15:54Z |
| publishDate | 2024 |
| publisher | Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1131522024-11-18T01:32:52Z http://psasir.upm.edu.my/id/eprint/113152/ Fractional block method for the solution of fractional order differential equations Noor, N.M. Yatim, S.A.M. Ibrahim, Z.B. The construction of the fourth-order 2-point Fractional Block Backward Differentiation Formula (2FBBDF(4)) to solve the fractional order differential equations (FDEs) is presented in this paper. The method is developed using the fractional linear multistep method (FLMM) linked with the linear difference operator. This paper aims to approximate the fractional order problems via 2FBBDF(4), which is normally used to solve ordinary differential equations. The criteria for the stability of the method are analyzed in order to solve FDE problems. Consequently, the method is determined to be A-stable for different values of α within the interval (0, 1). Then, Newton’s iteration is implemented in this method to solve the problems. Multiple numerical examples of linear, nonlinear, and system FDEs are provided for the scenario where the order α lies within the range of 0 and 1. Ultimately, the numerical results confirm that the proposed method performs at a similar level to the existing methods. Universiti Putra Malaysia 2024 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/113152/1/113152.pdf Noor, N.M. and Yatim, S.A.M. and Ibrahim, Z.B. (2024) Fractional block method for the solution of fractional order differential equations. Malaysian Journal of Mathematical Sciences, 18 (1). pp. 185-208. ISSN 1823-8343; eISSN: 2289-750X https://mjms.upm.edu.my/lihatmakalah.php?kod=2024/March/18/1/185-208 10.47836/mjms.18.1.11 |
| spellingShingle | Noor, N.M. Yatim, S.A.M. Ibrahim, Z.B. Fractional block method for the solution of fractional order differential equations |
| title | Fractional block method for the solution of fractional order differential equations |
| title_full | Fractional block method for the solution of fractional order differential equations |
| title_fullStr | Fractional block method for the solution of fractional order differential equations |
| title_full_unstemmed | Fractional block method for the solution of fractional order differential equations |
| title_short | Fractional block method for the solution of fractional order differential equations |
| title_sort | fractional block method for the solution of fractional order differential equations |
| url | http://psasir.upm.edu.my/id/eprint/113152/ http://psasir.upm.edu.my/id/eprint/113152/ http://psasir.upm.edu.my/id/eprint/113152/ http://psasir.upm.edu.my/id/eprint/113152/1/113152.pdf |