A robust multi-step predictor-corrector method for solving fractional order biological models
- 1Department of Computing, Mathematical and Statistical Sciences, University of Namibia
- 2Department of Mathematics and Applied Mathematics, University of the Western Cape
Abstract
This paper proposes a fractional Adams-type predictor-corrector scheme for solving nonlinear biological models involving Caputo derivatives of order 0<α ≤ 1 . The proposed method is formulated within a fractional Adams-type predictor-corrector framework by incorporating binomial coefficients derived from Euler’s gamma function. A three-step fractional Adams-type predictor is coupled with a two-step fractional corrector to construct the numerical scheme. Existence and uniqueness of solutions are established using fixed-point arguments, while consistency, stability, and convergence properties of the method are analysed. The numerical results indicate convergence behaviour approximately consistent with O(h2α ) for moderate and large fractional orders. Truncation and global error estimates are derived, and convergence rates are examined numerically using the double mesh principle. The performance of the proposed method is investigated using three representative fractional-order biological models, including ecological predator-prey dynamics and epidemiological SIR and SEIR systems. Numerical experiments demonstrate that the method provides stable and accurate numerical approximations for nonlinear models exhibiting memory effects. The results further illustrate the influence of the fractional order on the dynamical behaviour of the biological systems considered.
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BibTeX
@article{elago2026robust,
title = {{A robust multi-step predictor-corrector method for solving fractional order biological models}},
author = {David Elago and Samuel M. Nuugulu and Kailash C. Patidar and Frednard Gideon},
journal = {Scientific Reports},
year = {2026},
month = jul,
doi = {10.1038/s41598-026-63033-w},
url = {https://doi.org/10.1038/s41598-026-63033-w},
note = {CC BY},
}
RIS
TY - JOUR
TI - A robust multi-step predictor-corrector method for solving fractional order biological models
AU - David Elago
AU - Samuel M. Nuugulu
AU - Kailash C. Patidar
AU - Frednard Gideon
PY - 2026
DA - 2026/07/01
JO - Scientific Reports
DO - 10.1038/s41598-026-63033-w
UR - https://doi.org/10.1038/s41598-026-63033-w
AB - This paper proposes a fractional Adams-type predictor-corrector scheme for solving nonlinear biological models involving Caputo derivatives of order 0<α ≤ 1 . The proposed method is formulated within a fractional Adams-type predictor-corrector framework by incorporating binomial coefficients derived from Euler’s gamma function. A three-step fractional Adams-type predictor is coupled with a two-step fractional corrector to construct the numerical scheme. Existence and uniqueness of solutions are established using fixed-point arguments, while consistency, stability, and convergence properties of the method are analysed. The numerical results indicate convergence behaviour approximately consistent with O(h^2α ) for moderate and large fractional orders. Truncation and global error estimates are derived, and convergence rates are examined numerically using the double mesh principle. The performance of the proposed method is investigated using three representative fractional-order biological models, including ecological predator-prey dynamics and epidemiological SIR and SEIR systems. Numerical experiments demonstrate that the method provides stable and accurate numerical approximations for nonlinear models exhibiting memory effects. The results further illustrate the influence of the fractional order on the dynamical behaviour of the biological systems considered.
SN - 2045-2322
ER -