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Fractional block method for the solution of fractional order differential equations


Citation

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

Abstract

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.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
DOI Number: https://doi.org/10.47836/mjms.18.1.11
Publisher: Universiti Putra Malaysia
Keywords: Fractional block method; Fractional order; Linear multistep method; Single order FDEs; Stability
Depositing User: Mr. Mohamad Syahrul Nizam Md Ishak
Date Deposited: 18 Nov 2024 01:32
Last Modified: 18 Nov 2024 01:32
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.47836/mjms.18.1.11
URI: http://psasir.upm.edu.my/id/eprint/113152
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