numerical solution
conditions
idea
Numerical solution of fractional differential equations with Caputo derivative by using numerical fractional predict–correct technique
study
2022-03-18
convergence analysis
Applied Sciences
Caputo
fractional order
account
values
26
main objective
competencies
axis
equations
numerical examples
importance
Caputo derivative operator
true
medicine
operators
articles
objective
cases
order
derivatives
technique
fractional differential equations
real axis
analysis
Fractional differential equations have recently demonstrated their importance in a variety of fields, including medicine, applied sciences, and engineering. The main objective of this study is to propose an Adams-type multistep method for solving differential equations of fractional order. The method is developed by implementing the Lagrange interpolation and taking into account the idea of the Adams–Moulton method for fractional case. The fractional derivative applied in this study is in the Caputo derivative operator. The analysis of the proposed method is presented in terms of order of the method, order of accuracy, and convergence analysis, with the proposed method being proved to converge. The stability of the method is also examined, where the stability regions appear to be symmetric to the real axis for various values of α. In order to validate the competency of the proposed method, several numerical examples for solving linear and nonlinear fractional differential equations are included. The method will be presented in the numerical predict–correct technique for the condition where α∈(0,1)\documentclass[12pt]{minimal}
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\begin{document}$\alpha \in (0,1)$\end{document}, in which α represents the order of fractional derivatives of Dαy(t)\documentclass[12pt]{minimal}
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\begin{document}$D^{\alpha }y(t)$\end{document}.
Lagrange interpolation
terms of order
multistep methods
region
nonlinear fractional differential equations
Adams-Moulton method
variety of fields
2022-03-18
terms
2022-09-02T16:08
example
differential equations
https://scigraph.springernature.com/explorer/license/
https://doi.org/10.1186/s13662-022-03697-6
fractional derivative
fractional case
interpolation
variety
accuracy
field
stability
derivative operator
method
stability region
order of accuracy
article
engineering
science
solution
Springer Nature - SN SciGraph project
Nur Amirah
Zabidi
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia
Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia
Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia
1
Numerical and Computational Mathematics
10.1186/s13662-022-03697-6
doi
Majid
Zanariah Abdul
1687-1839
2731-4235
Advances in Continuous and Discrete Models
Springer Nature
Zarina Bibi
Ibrahim
dimensions_id
pub.1146389211
2022
Adem
Kilicman
Mathematical Sciences