Title
Approximation of Fractional Caputo Derivative of Variable Order and Variable Terminals with Application to Initial/Boundary Value Problems
Authors
[ 1 ] Instytut Analizy Konstrukcji, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | [ P ] employee
Scientific discipline (Law 2.0)
Year of publication
2025
Published in
Article type
scientific article
Publication language
english
Keywords
EN
- fractional calculus
- fractional differential equation
- fractional boundary value problem
- fractional initial value problem
- fractional derivative approximation
- fractional variable order
- variable terminal of fractional derivative
Abstract
EN This article presents a method for the approximate calculation of fractional Caputo derivatives, including a crucial aspect of the ability to handle arbitrary—even variable—terminals and order. The proposed method involves rearranging the fractional operator as a series of higher-order derivatives considered at a specific point. We demonstrate the effect of the number of terms included in the series expansion on the solution accuracy and error analysis. The advantage of the method is its simplicity and ease of implementation. Additionally, the method allows for a quick estimation of the fractional derivative by using a few first terms of the expansion. The elaborated algorithm is tested against a comprehensive series of illustrative examples, providing very good agreement with the exact/reference solutions. Furthermore, the application of the proposed method to fractional boundary/initial value problems is included.
Date of online publication
22.04.2025
Pages (from - to)
269-1 - 269-17
Comments
Article Number: 269
License type
CC BY (attribution alone)
Open Access Mode
open journal
Open Access Text Version
final published version
Date of Open Access to the publication
at the time of publication
Ministry points / journal
20
Impact Factor
3,6 [List 2023]
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