A comparative framework for convergence analysis of perturbation series techniques in nonlinear fractional quadratic differential equations

Dulfikar Jawad Hashim

PLOS ONE, 2025, vol. 20, issue 12, 1-12

Abstract: This study tackles the challenge of obtaining highly accurate approximate solutions for nonlinear fractional differential equations, which often lack exact solutions due to their inherent complexity. A unified perturbation framework is proposed based on homotopy topology theory, enabling multiple formulations depending on the number of convergence-control parameters. Through dynamic adjustment of these parameters, the Homotopy Method achieves enhanced precision, particularly for fractional-order models exhibiting long-memory behavior. Numerical results clearly demonstrate that increasing the number of convergence parameters leads to significantly improved accuracy. Supported by detailed graphs and tables, the proposed approach proves to be a flexible, robust, and reliable tool for solving nonlinear fractional differential equations.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0337884 (text/html)
https://journals.plos.org/plosone/article/file?id= ... 37884&type=printable (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0337884

DOI: 10.1371/journal.pone.0337884

Access Statistics for this article

More articles in PLOS ONE from Public Library of Science
Bibliographic data for series maintained by plosone ().